In this paper,a distributed adaptive dynamic programming(ADP)framework based on value iteration is proposed for multi-player differential games.In the game setting,players have no access to the information of others&#...In this paper,a distributed adaptive dynamic programming(ADP)framework based on value iteration is proposed for multi-player differential games.In the game setting,players have no access to the information of others'system parameters or control laws.Each player adopts an on-policy value iteration algorithm as the basic learning framework.To deal with the incomplete information structure,players collect a period of system trajectory data to compensate for the lack of information.The policy updating step is implemented by a nonlinear optimization problem aiming to search for the proximal admissible policy.Theoretical analysis shows that by adopting proximal policy searching rules,the approximated policies can converge to a neighborhood of equilibrium policies.The efficacy of our method is illustrated by three examples,which also demonstrate that the proposed method can accelerate the learning process compared with the centralized learning framework.展开更多
This paper introduces an interval valued linear fractional programming problem (IVLFP). An IVLFP is a linear frac-tional programming problem with interval coefficients in the objective function. It is proved that we c...This paper introduces an interval valued linear fractional programming problem (IVLFP). An IVLFP is a linear frac-tional programming problem with interval coefficients in the objective function. It is proved that we can convert an IVLFP to an optimization problem with interval valued objective function which its bounds are linear fractional functions. Also there is a discussion for the solutions of this kind of optimization problem.展开更多
We propose a stochastic level value approximation method for a quadratic integer convex minimizing problem in this paper. This method applies an importance sampling technique, and make use of the cross-entropy method ...We propose a stochastic level value approximation method for a quadratic integer convex minimizing problem in this paper. This method applies an importance sampling technique, and make use of the cross-entropy method to update the sample density functions. We also prove the asymptotic convergence of this algorithm, and report some numerical results to illuminate its effectiveness.展开更多
Background: Anti-programmed death-1/programmed death-ligand 1(PD-1/PD-L1) immunotherapy has been proved to be effective on gastric cancer in ongoing clinical trials. However, the value of PD-L1 in predicting responses...Background: Anti-programmed death-1/programmed death-ligand 1(PD-1/PD-L1) immunotherapy has been proved to be effective on gastric cancer in ongoing clinical trials. However, the value of PD-L1 in predicting responses of patients with gastric cancer to anti-PD-1/PD-L1 immunotherapy is controversial. Some studies suggested that intra-and inter-tumoral heterogeneity of PD-L1 expression might explain the controversy.This study aimed to analyze the expression of PD-L1, PD-L2, and PD-1 as well as CD8(+) T-cell density in primary tumors and lymph nodes from patients with stage T1-4 N+M0 gastric adenocarcinoma to explore the heterogeneity of PD-1 signaling pathway molecules.Methods: In primary tumors and metastatic as well as non-metastatic lymph nodes from patients with stage T1-4 N+M0 gastric adenocarcinoma, we detected PD-L1 and PD-L2 expression with immunohistochemistry. CD8(+)T-cell density in primary tumors and PD-1 expression on CD8(+)T cells were detected with immunofluorescence. Univariate analysis was used to determine the prognostic values of them. Cox proportional hazard regression model was used to identify independent risk factors that affect patients' overall survival and disease-free survival.Results: Among 119 eligible patients who had undergone surgical resection, the positive rate of PD-L1 was higher in metastatic lymph nodes than in primary tumors(45.4% vs. 38.7%, P = 0.005); the positive rate of PD-1 on CD8(+)T cells was significantly higher in primary tumors and metastatic lymph nodes than in tumor-free lymph nodes(both P < 0.001). The intensity of PD-1 expression on CD8(+) T cells in primary tumors and in metastatic lymph nodes were stronger than that in tumor-free lymph nodes from the same patient. Beside, the positive rate of PD-L2 did not show any differences between primary tumors and metastatic lymph nodes. In multivariate analysis, PD-L1 expression,PD-L2 expression, a low density of CD8(+) T cells in primary tumors, and PD-1 expression on CD8(+) T cells in primary tumors were associated with poor prognosis.Conclusion: The expression of PD-L1 is heterogeneous in primary tumors and in metastatic lymph nodes from patients with stageT1-4 N+M0 gastric adenocarcinoma, which might explain the inconsistent results in assessing the prognostic value of PD-L1 expression in previous studies.展开更多
An uncertain multi-objective programming problem is a special type of mathematical multi-objective programming involving uncertain variables. This type of problem is important because there are several uncertain varia...An uncertain multi-objective programming problem is a special type of mathematical multi-objective programming involving uncertain variables. This type of problem is important because there are several uncertain variables in real-world problems.Therefore, research on the uncertain multi-objective programming problem is highly relevant, particularly those problems whose objective functions are correlated. In this paper, an approach that solves an uncertain multi-objective programming problem under the expected-variance value criterion is proposed. First, we define the basic framework of the approach and review concepts such as a Pareto efficient solution and expected-variance value criterion using an order relation between various uncertain variables.Second, the uncertain multi-objective problem is converted into an uncertain single-objective programming problem via a linear weighted method or ideal point method. Then the problem is transformed into a deterministic single objective programming problem under the expected-variance value criterion. Third, four lemmas and two theorems are proved to illustrate that the optimal solution of the deterministic single-objective programming problem is an efficient solution to the original uncertainty problem. Finally, two numerical examples are presented to validate the effectiveness of the proposed approach.展开更多
This paper studies data-driven learning-based methods for the finite-horizon optimal control of linear time-varying discretetime systems. First, a novel finite-horizon Policy Iteration (PI) method for linear time-vary...This paper studies data-driven learning-based methods for the finite-horizon optimal control of linear time-varying discretetime systems. First, a novel finite-horizon Policy Iteration (PI) method for linear time-varying discrete-time systems is presented. Its connections with existing in finite-horizon PI methods are discussed. Then, both data-drive n off-policy PI and Value Iteration (VI) algorithms are derived to find approximate optimal controllers when the system dynamics is completely unknown. Under mild conditions, the proposed data-driven off-policy algorithms converge to the optimal solution. Finally, the effectiveness and feasibility of the developed methods are validated by a practical example of spacecraft attitude control.展开更多
In this paper, optimality conditions for multiobjective programming problems having V-invex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modif...In this paper, optimality conditions for multiobjective programming problems having V-invex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modification of the objective function.Furthermore, a (α, η)-Lagrange function is introduced for a constructed multiobjective programming problem, and a new type of saddle point is introduced. Some results for the new type of saddle point are given.展开更多
In order to address the output feedback issue for linear discrete-time systems, this work suggests a brand-new adaptive dynamic programming(ADP) technique based on the internal model principle(IMP). The proposed metho...In order to address the output feedback issue for linear discrete-time systems, this work suggests a brand-new adaptive dynamic programming(ADP) technique based on the internal model principle(IMP). The proposed method, termed as IMP-ADP, does not require complete state feedback-merely the measurement of input and output data. More specifically, based on the IMP, the output control problem can first be converted into a stabilization problem. We then design an observer to reproduce the full state of the system by measuring the inputs and outputs. Moreover, this technique includes both a policy iteration algorithm and a value iteration algorithm to determine the optimal feedback gain without using a dynamic system model. It is important that with this concept one does not need to solve the regulator equation. Finally, this control method was tested on an inverter system of grid-connected LCLs to demonstrate that the proposed method provides the desired performance in terms of both tracking and disturbance rejection.展开更多
To overcome the defects that the traditional ap-proach for multi-objective programming under uncertain ran-dom environment(URMOP)neglects the randomness and uncer-tainty of the problem and the volatility of the result...To overcome the defects that the traditional ap-proach for multi-objective programming under uncertain ran-dom environment(URMOP)neglects the randomness and uncer-tainty of the problem and the volatility of the results,a new ap-proach is proposed based on expected value-standard devi-ation value criterion(C_(ESD) criterion).Firstly,the effective solution to the URMOP problem is defined;then,by applying sequence relationship between the uncertain random variables,the UR-MOP problem is transformed into a single-objective program-ming(SOP)under uncertain random environment(URSOP),which are transformed into a deterministic counterpart based on the C_(ESD) criterion.Then the validity of the new approach is proved that the optimal solution to the SOP problem is also effi-cient for the URMOP problem;finally,a numerical example and a case application are presented to show the effectiveness of the new approach.展开更多
Despite it is often available in practice, information of optimal value of linear programming problems is ignored by conventional simplex algorithms. To speed up solution process, we propose in this paper some vari...Despite it is often available in practice, information of optimal value of linear programming problems is ignored by conventional simplex algorithms. To speed up solution process, we propose in this paper some variants of the bisection algorithm, explo展开更多
To properly describe and solve complex decision problems, research on theoretical properties and solution of mixed-integer quadratic programs is becoming very important. We establish in this paper different Lipschitz-...To properly describe and solve complex decision problems, research on theoretical properties and solution of mixed-integer quadratic programs is becoming very important. We establish in this paper different Lipschitz-type continuity results about the optimal value function and optimal solutions of mixed-integer parametric quadratic programs with parameters in the linear part of the objective function and in the right-hand sides of the linear constraints. The obtained results extend some existing results for continuous quadratic programs, and, more importantly, lay the foundation for further theoretical study and corresponding algorithm analysis on mixed-integer quadratic programs.展开更多
When all the involved data in indefinite quadratic programs change simultaneously, we show the locally Lipschtiz continuity of the KKT set of the quadratic programming problem firstly, then we establish the locally Li...When all the involved data in indefinite quadratic programs change simultaneously, we show the locally Lipschtiz continuity of the KKT set of the quadratic programming problem firstly, then we establish the locally Lipschtiz continuity of the KKT solution set. Finally, the similar conclusion for the corresponding optimal value function is obtained.展开更多
Bilevel linear programming, which consists of the objective functions of the upper level and lower level, is a useful tool for modeling decentralized decision problems. Various methods are proposed for solving this pr...Bilevel linear programming, which consists of the objective functions of the upper level and lower level, is a useful tool for modeling decentralized decision problems. Various methods are proposed for solving this problem. Of all the algorithms, the ge- netic algorithm is an alternative to conventional approaches to find the solution of the bilevel linear programming. In this paper, we describe an adaptive genetic algorithm for solving the bilevel linear programming problem to overcome the difficulty of determining the probabilities of crossover and mutation. In addition, some techniques are adopted not only to deal with the difficulty that most of the chromosomes maybe infeasible in solving constrained optimization problem with genetic algorithm but also to improve the efficiency of the algorithm. The performance of this proposed algorithm is illustrated by the examples from references.展开更多
A second-order Mond-Weir type dual problem is formulated for a class of continuous programming problems in which both objective and constraint functions contain support functions;hence it is nondifferentiable. Under s...A second-order Mond-Weir type dual problem is formulated for a class of continuous programming problems in which both objective and constraint functions contain support functions;hence it is nondifferentiable. Under second-order strict pseudoinvexity, second-order pseudoinvexity and second-order quasi-invexity assumptions on functionals, weak, strong, strict converse and converse duality theorems are established for this pair of dual continuous programming problems. Special cases are deduced and a pair of dual continuous problems with natural boundary values is constructed. A close relationship between the duality results of our problems and those of the corresponding (static) nonlinear programming problem with support functions is briefly outlined.展开更多
A second-order dual problem is formulated for a class of continuous programming problem in which both objective and constrained functions contain support functions, hence it is nondifferentiable. Under second-order in...A second-order dual problem is formulated for a class of continuous programming problem in which both objective and constrained functions contain support functions, hence it is nondifferentiable. Under second-order invexity and second-order pseudoinvexity, weak, strong and converse duality theorems are established for this pair of dual problems. Special cases are deduced and a pair of dual continuous problems with natural boundary values is constructed. A close relationship between duality results of our problems and those of the corresponding (static) nonlinear programming problem with support functions is briefly outlined.展开更多
The current structure of Landmark University (LU) was induced by raising a generation of solution providers through a qualitative and life-applicable training system that focuses on values and creative knowledge by ma...The current structure of Landmark University (LU) was induced by raising a generation of solution providers through a qualitative and life-applicable training system that focuses on values and creative knowledge by making it more responsive and relevant to the modern-day demands of demonstration, industrialization and development. The challenge facing Landmark University is the question of which of its numerous projects they should invest to give maximum output with minimum input. In this paper, we maximize the Net Present Value (NPV) and maintain the net discount cash overflow of each project per period as contained and extracted as the secondary data of cash inflows of the Landmark University (LU) monthly financial statement and annual reports from 2012 to 2017 of which the documents have been regrouped as small and large scale projects as many enterprises make more use of the trial-and-error method and as such firms have been finding it difficult in allocating scarce resources in a manner that will ensure profit maximization and/or cost minimization with a simple and accurate decision making by the company through an optimization principle in selecting LU project under multi-period capital rationing using linear programming (LP) and integer programming (IP). The annual net cash flow which is the difference between the cash inflows and cash outflows during each period for the project was estimated and recorded. The discount factors were estimated at cost of capital of 10% for each cash flow per period with the corresponding NPV at 10% which revealed that the optimal decision achieves maximum returns of $110 × 102 and this assisted the project manager to select a large number of the variable projects that can maximize the profit which is far better than relying on an ad-hoc judgmental approach to project investment that could have cost 160 × 102 for the same project. Sensitivity analysis on the project parameters are also carried out to test the extent to which project selection is sensitive to changes in the parameters of the system revealed that a little reduction and or addition of reduced cost by certain amount or percentages to its corresponding coefficient in the objective function effect no changes in the shadow prices with solution values for variables (x1), (x4), (x5) and the optimal objective function.展开更多
Many Optimization problems in engineering and economic involve the challenging task of pondering both conflicting goals and random data. In this paper, we give an up-to-date overview of how important ideas from optimi...Many Optimization problems in engineering and economic involve the challenging task of pondering both conflicting goals and random data. In this paper, we give an up-to-date overview of how important ideas from optimization, probability theory and multicriteria decision analysis are interwoven to address situations where the presence of several objective functions and the stochastic nature of data are under one roof in a linear optimization context. In this way users of these models are not bound to caricature their problems by arbitrarily squeezing different objective functions into one and by blindly accepting fixed values in lieu of imprecise ones.展开更多
The idea of equality is an important part of Marxist theory system and an ideal creed pursued by mankind.Marx’s thought of equality is reflected in the Criticism of Gotha Program.Marx’s criticism of“absolute labor ...The idea of equality is an important part of Marxist theory system and an ideal creed pursued by mankind.Marx’s thought of equality is reflected in the Criticism of Gotha Program.Marx’s criticism of“absolute labor income”elaborates the distribution theory of the two stages of communism.The criticism of“labor determinism”defends the fundamental principle of“production decides distribution”.It criticizes the essence of“free education for all”and puts forward the idea of education equality in an ideal society.In the new era,it is helpful to improve the equality system and protect the basic rights of citizens to review their equality thoughts.What’s more,it is also helpful to develop productive forces Vigorously and consolidate the equal foundation of socialist countries.We will deepen the reform of education and improve the sense of happiness of education equality.展开更多
Objective:To monitor the incidence of immune-related adverse events(irAEs)in patients treated with immune checkpoint inhibitors(ICIs)and programmed cell death protein-1(PD-1),and to evaluate the effectiveness of nursi...Objective:To monitor the incidence of immune-related adverse events(irAEs)in patients treated with immune checkpoint inhibitors(ICIs)and programmed cell death protein-1(PD-1),and to evaluate the effectiveness of nursing interventions using a quantitative scoring system.Methods:A retrospective analysis was performed on 65 cancer patients who received PD-1 therapy at the Oncology Department of Baotou Cancer Hospital from December 2023 to December 2024.The study examined the clinical features and blood test results related to irAEs.The National Cancer Institute’s Common Terminology Criteria for Adverse Events(NCI-CTCAE)was used to grade the severity of these events,which were classified into five levels.Based on the NCI-CTCAE scores,appropriate nursing measures were implemented,and a comprehensive risk assessment framework was developed.Results:The study group showed lower complication rates,overall incidence,and average hospital stay compared to the control group(P<0.05).Among the 65 patients,twenty-eight(43.07%)experienced a total of 35 irAEs,with 2(5.71%)being grade 3 or 4.The most frequent irAEs were dermatological conditions(34.29%),particularly rash with itching.The occurrence of irAEs did not correlate with patient gender,age,blood parameters(hemoglobin,white blood cell count,platelet count,etc.),or liver function(P>0.05),but it was associated with tumor type(P<0.05).Conclusion:PD-1 treatment is generally safe,with a low incidence of severe(grade 3 or higher)irAEs.Close monitoring is essential to ensure early detection,intervention,and management of irAEs,thereby maintaining a low level of adverse events and enhancing the safety and efficacy of PD-1 therapy.Implementing a quantitative risk scoring system for nursing care can decrease the rate of complications,enhance patient safety,and potentially reduce hospital stays and medical costs.展开更多
基金supported by the Aeronautical Science Foundation of China(20220001057001)an Open Project of the National Key Laboratory of Air-based Information Perception and Fusion(202437)
文摘In this paper,a distributed adaptive dynamic programming(ADP)framework based on value iteration is proposed for multi-player differential games.In the game setting,players have no access to the information of others'system parameters or control laws.Each player adopts an on-policy value iteration algorithm as the basic learning framework.To deal with the incomplete information structure,players collect a period of system trajectory data to compensate for the lack of information.The policy updating step is implemented by a nonlinear optimization problem aiming to search for the proximal admissible policy.Theoretical analysis shows that by adopting proximal policy searching rules,the approximated policies can converge to a neighborhood of equilibrium policies.The efficacy of our method is illustrated by three examples,which also demonstrate that the proposed method can accelerate the learning process compared with the centralized learning framework.
文摘This paper introduces an interval valued linear fractional programming problem (IVLFP). An IVLFP is a linear frac-tional programming problem with interval coefficients in the objective function. It is proved that we can convert an IVLFP to an optimization problem with interval valued objective function which its bounds are linear fractional functions. Also there is a discussion for the solutions of this kind of optimization problem.
基金Project supported by the National Natural Science Foundation of China (No.10671117)Shanghai Leading Academic Discipline Project (No.J050101)the Youth Science Foundation of Hunan Education Department of China (No.06B037)
文摘We propose a stochastic level value approximation method for a quadratic integer convex minimizing problem in this paper. This method applies an importance sampling technique, and make use of the cross-entropy method to update the sample density functions. We also prove the asymptotic convergence of this algorithm, and report some numerical results to illuminate its effectiveness.
文摘Background: Anti-programmed death-1/programmed death-ligand 1(PD-1/PD-L1) immunotherapy has been proved to be effective on gastric cancer in ongoing clinical trials. However, the value of PD-L1 in predicting responses of patients with gastric cancer to anti-PD-1/PD-L1 immunotherapy is controversial. Some studies suggested that intra-and inter-tumoral heterogeneity of PD-L1 expression might explain the controversy.This study aimed to analyze the expression of PD-L1, PD-L2, and PD-1 as well as CD8(+) T-cell density in primary tumors and lymph nodes from patients with stage T1-4 N+M0 gastric adenocarcinoma to explore the heterogeneity of PD-1 signaling pathway molecules.Methods: In primary tumors and metastatic as well as non-metastatic lymph nodes from patients with stage T1-4 N+M0 gastric adenocarcinoma, we detected PD-L1 and PD-L2 expression with immunohistochemistry. CD8(+)T-cell density in primary tumors and PD-1 expression on CD8(+)T cells were detected with immunofluorescence. Univariate analysis was used to determine the prognostic values of them. Cox proportional hazard regression model was used to identify independent risk factors that affect patients' overall survival and disease-free survival.Results: Among 119 eligible patients who had undergone surgical resection, the positive rate of PD-L1 was higher in metastatic lymph nodes than in primary tumors(45.4% vs. 38.7%, P = 0.005); the positive rate of PD-1 on CD8(+)T cells was significantly higher in primary tumors and metastatic lymph nodes than in tumor-free lymph nodes(both P < 0.001). The intensity of PD-1 expression on CD8(+) T cells in primary tumors and in metastatic lymph nodes were stronger than that in tumor-free lymph nodes from the same patient. Beside, the positive rate of PD-L2 did not show any differences between primary tumors and metastatic lymph nodes. In multivariate analysis, PD-L1 expression,PD-L2 expression, a low density of CD8(+) T cells in primary tumors, and PD-1 expression on CD8(+) T cells in primary tumors were associated with poor prognosis.Conclusion: The expression of PD-L1 is heterogeneous in primary tumors and in metastatic lymph nodes from patients with stageT1-4 N+M0 gastric adenocarcinoma, which might explain the inconsistent results in assessing the prognostic value of PD-L1 expression in previous studies.
基金supported by the National Natural Science Foundation of China(71601183 71571190)
文摘An uncertain multi-objective programming problem is a special type of mathematical multi-objective programming involving uncertain variables. This type of problem is important because there are several uncertain variables in real-world problems.Therefore, research on the uncertain multi-objective programming problem is highly relevant, particularly those problems whose objective functions are correlated. In this paper, an approach that solves an uncertain multi-objective programming problem under the expected-variance value criterion is proposed. First, we define the basic framework of the approach and review concepts such as a Pareto efficient solution and expected-variance value criterion using an order relation between various uncertain variables.Second, the uncertain multi-objective problem is converted into an uncertain single-objective programming problem via a linear weighted method or ideal point method. Then the problem is transformed into a deterministic single objective programming problem under the expected-variance value criterion. Third, four lemmas and two theorems are proved to illustrate that the optimal solution of the deterministic single-objective programming problem is an efficient solution to the original uncertainty problem. Finally, two numerical examples are presented to validate the effectiveness of the proposed approach.
基金The work of B. Pang and Z.-P. Jiang has been supported in part by the National Science Foundation (No. ECCS-1501044).
文摘This paper studies data-driven learning-based methods for the finite-horizon optimal control of linear time-varying discretetime systems. First, a novel finite-horizon Policy Iteration (PI) method for linear time-varying discrete-time systems is presented. Its connections with existing in finite-horizon PI methods are discussed. Then, both data-drive n off-policy PI and Value Iteration (VI) algorithms are derived to find approximate optimal controllers when the system dynamics is completely unknown. Under mild conditions, the proposed data-driven off-policy algorithms converge to the optimal solution. Finally, the effectiveness and feasibility of the developed methods are validated by a practical example of spacecraft attitude control.
基金Supported by the National Natural Science Foundation of China(19871009)
文摘In this paper, optimality conditions for multiobjective programming problems having V-invex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modification of the objective function.Furthermore, a (α, η)-Lagrange function is introduced for a constructed multiobjective programming problem, and a new type of saddle point is introduced. Some results for the new type of saddle point are given.
基金supported by the National Science Fund for Distinguished Young Scholars (62225303)the Fundamental Research Funds for the Central Universities (buctrc202201)+1 种基金China Scholarship Council,and High Performance Computing PlatformCollege of Information Science and Technology,Beijing University of Chemical Technology。
文摘In order to address the output feedback issue for linear discrete-time systems, this work suggests a brand-new adaptive dynamic programming(ADP) technique based on the internal model principle(IMP). The proposed method, termed as IMP-ADP, does not require complete state feedback-merely the measurement of input and output data. More specifically, based on the IMP, the output control problem can first be converted into a stabilization problem. We then design an observer to reproduce the full state of the system by measuring the inputs and outputs. Moreover, this technique includes both a policy iteration algorithm and a value iteration algorithm to determine the optimal feedback gain without using a dynamic system model. It is important that with this concept one does not need to solve the regulator equation. Finally, this control method was tested on an inverter system of grid-connected LCLs to demonstrate that the proposed method provides the desired performance in terms of both tracking and disturbance rejection.
基金supported by the National Natural Science Foundation of China(72001213)the basic research program of Natural Science of Shaanxi Province,China(2021JQ-369).
文摘To overcome the defects that the traditional ap-proach for multi-objective programming under uncertain ran-dom environment(URMOP)neglects the randomness and uncer-tainty of the problem and the volatility of the results,a new ap-proach is proposed based on expected value-standard devi-ation value criterion(C_(ESD) criterion).Firstly,the effective solution to the URMOP problem is defined;then,by applying sequence relationship between the uncertain random variables,the UR-MOP problem is transformed into a single-objective program-ming(SOP)under uncertain random environment(URSOP),which are transformed into a deterministic counterpart based on the C_(ESD) criterion.Then the validity of the new approach is proved that the optimal solution to the SOP problem is also effi-cient for the URMOP problem;finally,a numerical example and a case application are presented to show the effectiveness of the new approach.
文摘Despite it is often available in practice, information of optimal value of linear programming problems is ignored by conventional simplex algorithms. To speed up solution process, we propose in this paper some variants of the bisection algorithm, explo
基金Supported by the National Natural Science Foundation of China(10571141,70971109)the Key Projectof the National Natural Science Foundation of China(70531030)
文摘To properly describe and solve complex decision problems, research on theoretical properties and solution of mixed-integer quadratic programs is becoming very important. We establish in this paper different Lipschitz-type continuity results about the optimal value function and optimal solutions of mixed-integer parametric quadratic programs with parameters in the linear part of the objective function and in the right-hand sides of the linear constraints. The obtained results extend some existing results for continuous quadratic programs, and, more importantly, lay the foundation for further theoretical study and corresponding algorithm analysis on mixed-integer quadratic programs.
基金Supported by the National Natural Science Foundation of China(10571141,70971109,71371152)supported by the Talents Fund of Xi’an Polytechnic University(BS1320)the Mathematics Discipline Development Fund of Xi’an Ploytechnic University(107090701)
文摘When all the involved data in indefinite quadratic programs change simultaneously, we show the locally Lipschtiz continuity of the KKT set of the quadratic programming problem firstly, then we establish the locally Lipschtiz continuity of the KKT solution set. Finally, the similar conclusion for the corresponding optimal value function is obtained.
基金the National Natural Science Foundation of China(Nos.60574071 and70771080)
文摘Bilevel linear programming, which consists of the objective functions of the upper level and lower level, is a useful tool for modeling decentralized decision problems. Various methods are proposed for solving this problem. Of all the algorithms, the ge- netic algorithm is an alternative to conventional approaches to find the solution of the bilevel linear programming. In this paper, we describe an adaptive genetic algorithm for solving the bilevel linear programming problem to overcome the difficulty of determining the probabilities of crossover and mutation. In addition, some techniques are adopted not only to deal with the difficulty that most of the chromosomes maybe infeasible in solving constrained optimization problem with genetic algorithm but also to improve the efficiency of the algorithm. The performance of this proposed algorithm is illustrated by the examples from references.
文摘A second-order Mond-Weir type dual problem is formulated for a class of continuous programming problems in which both objective and constraint functions contain support functions;hence it is nondifferentiable. Under second-order strict pseudoinvexity, second-order pseudoinvexity and second-order quasi-invexity assumptions on functionals, weak, strong, strict converse and converse duality theorems are established for this pair of dual continuous programming problems. Special cases are deduced and a pair of dual continuous problems with natural boundary values is constructed. A close relationship between the duality results of our problems and those of the corresponding (static) nonlinear programming problem with support functions is briefly outlined.
文摘A second-order dual problem is formulated for a class of continuous programming problem in which both objective and constrained functions contain support functions, hence it is nondifferentiable. Under second-order invexity and second-order pseudoinvexity, weak, strong and converse duality theorems are established for this pair of dual problems. Special cases are deduced and a pair of dual continuous problems with natural boundary values is constructed. A close relationship between duality results of our problems and those of the corresponding (static) nonlinear programming problem with support functions is briefly outlined.
文摘The current structure of Landmark University (LU) was induced by raising a generation of solution providers through a qualitative and life-applicable training system that focuses on values and creative knowledge by making it more responsive and relevant to the modern-day demands of demonstration, industrialization and development. The challenge facing Landmark University is the question of which of its numerous projects they should invest to give maximum output with minimum input. In this paper, we maximize the Net Present Value (NPV) and maintain the net discount cash overflow of each project per period as contained and extracted as the secondary data of cash inflows of the Landmark University (LU) monthly financial statement and annual reports from 2012 to 2017 of which the documents have been regrouped as small and large scale projects as many enterprises make more use of the trial-and-error method and as such firms have been finding it difficult in allocating scarce resources in a manner that will ensure profit maximization and/or cost minimization with a simple and accurate decision making by the company through an optimization principle in selecting LU project under multi-period capital rationing using linear programming (LP) and integer programming (IP). The annual net cash flow which is the difference between the cash inflows and cash outflows during each period for the project was estimated and recorded. The discount factors were estimated at cost of capital of 10% for each cash flow per period with the corresponding NPV at 10% which revealed that the optimal decision achieves maximum returns of $110 × 102 and this assisted the project manager to select a large number of the variable projects that can maximize the profit which is far better than relying on an ad-hoc judgmental approach to project investment that could have cost 160 × 102 for the same project. Sensitivity analysis on the project parameters are also carried out to test the extent to which project selection is sensitive to changes in the parameters of the system revealed that a little reduction and or addition of reduced cost by certain amount or percentages to its corresponding coefficient in the objective function effect no changes in the shadow prices with solution values for variables (x1), (x4), (x5) and the optimal objective function.
文摘Many Optimization problems in engineering and economic involve the challenging task of pondering both conflicting goals and random data. In this paper, we give an up-to-date overview of how important ideas from optimization, probability theory and multicriteria decision analysis are interwoven to address situations where the presence of several objective functions and the stochastic nature of data are under one roof in a linear optimization context. In this way users of these models are not bound to caricature their problems by arbitrarily squeezing different objective functions into one and by blindly accepting fixed values in lieu of imprecise ones.
基金“Theoretical and Practical Research on Regional Education Quality and Balanced Development”(2021B179),a key project of Guangxi Education Science Planning.
文摘The idea of equality is an important part of Marxist theory system and an ideal creed pursued by mankind.Marx’s thought of equality is reflected in the Criticism of Gotha Program.Marx’s criticism of“absolute labor income”elaborates the distribution theory of the two stages of communism.The criticism of“labor determinism”defends the fundamental principle of“production decides distribution”.It criticizes the essence of“free education for all”and puts forward the idea of education equality in an ideal society.In the new era,it is helpful to improve the equality system and protect the basic rights of citizens to review their equality thoughts.What’s more,it is also helpful to develop productive forces Vigorously and consolidate the equal foundation of socialist countries.We will deepen the reform of education and improve the sense of happiness of education equality.
基金Baotou City Health Science and Technology Plan(Project No.:2023wsjkkj109)。
文摘Objective:To monitor the incidence of immune-related adverse events(irAEs)in patients treated with immune checkpoint inhibitors(ICIs)and programmed cell death protein-1(PD-1),and to evaluate the effectiveness of nursing interventions using a quantitative scoring system.Methods:A retrospective analysis was performed on 65 cancer patients who received PD-1 therapy at the Oncology Department of Baotou Cancer Hospital from December 2023 to December 2024.The study examined the clinical features and blood test results related to irAEs.The National Cancer Institute’s Common Terminology Criteria for Adverse Events(NCI-CTCAE)was used to grade the severity of these events,which were classified into five levels.Based on the NCI-CTCAE scores,appropriate nursing measures were implemented,and a comprehensive risk assessment framework was developed.Results:The study group showed lower complication rates,overall incidence,and average hospital stay compared to the control group(P<0.05).Among the 65 patients,twenty-eight(43.07%)experienced a total of 35 irAEs,with 2(5.71%)being grade 3 or 4.The most frequent irAEs were dermatological conditions(34.29%),particularly rash with itching.The occurrence of irAEs did not correlate with patient gender,age,blood parameters(hemoglobin,white blood cell count,platelet count,etc.),or liver function(P>0.05),but it was associated with tumor type(P<0.05).Conclusion:PD-1 treatment is generally safe,with a low incidence of severe(grade 3 or higher)irAEs.Close monitoring is essential to ensure early detection,intervention,and management of irAEs,thereby maintaining a low level of adverse events and enhancing the safety and efficacy of PD-1 therapy.Implementing a quantitative risk scoring system for nursing care can decrease the rate of complications,enhance patient safety,and potentially reduce hospital stays and medical costs.
