To overcome inefficiency in traditional logic programming, a declarative programming language COPS is designed based on the notion of concurrent constraint programming (CCP). The improvement is achieved by the adoptio...To overcome inefficiency in traditional logic programming, a declarative programming language COPS is designed based on the notion of concurrent constraint programming (CCP). The improvement is achieved by the adoption of constraint-based heuristic strategy and the introduction of deterministic components in the framework of CCP. Syntax specification and an operational semantic description are presented.展开更多
This paper addresses the issue of checking consistency in information models. A method based on constraint programming is proposed for identifying inconsistency or proving consistency in information models. The system...This paper addresses the issue of checking consistency in information models. A method based on constraint programming is proposed for identifying inconsistency or proving consistency in information models. The system described here checks information models written in the ISO standard information modelling language EXPRESS. EXPRESS is part of the ISO STEP standard used in the manufacturing and process industries. This paper describes the checking procedure, including EXPRESS model formalization, constraint satisfaction problem (CSP) derivation from the formalized model and satisfaction checking of the derived CSPs. This paper shows a new domain in which constraint programming can be exploited as model verification and validation.展开更多
this paper,we propose a class of smoothing-regularization methods for solving the mathematical programming with vanishing constraints.These methods include the smoothing-regularization method proposed by Kanzow et al....this paper,we propose a class of smoothing-regularization methods for solving the mathematical programming with vanishing constraints.These methods include the smoothing-regularization method proposed by Kanzow et al.in[Comput.Optim.Appl.,2013,55(3):733-767]as a special case.Under the weaker conditions than the ones that have been used by Kanzow et al.in 2013,we prove that the Mangasarian-Fromovitz constraint qualification holds at the feasible points of smoothing-regularization problem.We also analyze that the convergence behavior of the proposed smoothing-regularization method under mild conditions,i.e.,any accumulation point of the stationary point sequence for the smoothing-regularization problem is a strong stationary point.Finally,numerical experiments are given to show the efficiency of the proposed methods.展开更多
In real production,machines are operated by workers,and the constraints of worker flexibility should be considered.The flexible job shop scheduling problem with both machine and worker resources(DRCFJSP)has become a r...In real production,machines are operated by workers,and the constraints of worker flexibility should be considered.The flexible job shop scheduling problem with both machine and worker resources(DRCFJSP)has become a research hotspot in recent years.In this paper,DRCFJSP with the objective of minimizing the makespan is studied,and it should solve three sub-problems:machine allocation,worker allocation,and operations sequencing.To solve DRCFJSP,a novel hybrid algorithm(CEAM-CP)of cooperative evolutionary algorithm with multiple populations(CEAM)and constraint programming(CP)is proposed.Specifically,the CEAM-CP algorithm is comprised of two main stages.In the first stage,CEAM is used based on three-layer encoding and full active decoding.Moreover,CEAM has three populations,each of which corresponds to one layer encoding and determines one sub-problem.Moreover,each population evolves cooperatively by multiple cross operations.To further improve the solution quality obtained by CEAM,CP is adopted in the second stage.Experiments are conducted on 13 benchmark instances to assess the effectiveness of multiple crossover operations,CP,and CEAM-CP.Most importantly,the proposed CEAM-CP improves 9 best-known solutions out of 13 benchmark instances.展开更多
A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forc...A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forced to be integer. An integer coding for upper level variables is adopted, and then a discrete differential evolution algorithm with an improved feasibility-based comparison is developed to directly explore the integer solution at the upper level. For a given upper level integer variable, the lower level integer programming problem is solved by the existing branch and bound algorithm to obtain the optimal integer solution at the lower level. In the same framework of the algorithm, two other constraint handling methods, i.e. the penalty function method and the feasibility-based comparison method are also tested. The experimental results demonstrate that the discrete differential evolution algorithm with different constraint handling methods is effective in finding the global optimal integer solutions, but the improved constraint handling method performs better than two compared constraint handling methods.展开更多
Mathematical programs with complementarity constraints(MPCC) is an important subclass of MPEC.It is a natural way to solve MPCC by constructing a suitable approximation of the primal problem.In this paper,we propose a...Mathematical programs with complementarity constraints(MPCC) is an important subclass of MPEC.It is a natural way to solve MPCC by constructing a suitable approximation of the primal problem.In this paper,we propose a new smoothing method for MPCC by using the aggregation technique.A new SQP algorithm for solving the MPCC problem is presented.At each iteration,the master direction is computed by solving a quadratic program,and the revised direction for avoiding the Maratos effect is generated by an explicit formula.As the non-degeneracy condition holds and the smoothing parameter tends to zero,the proposed SQP algorithm converges globally to an S-stationary point of the MPEC problem,its convergence rate is superlinear.Some preliminary numerical results are reported.展开更多
In this paper, we describe a successive approximation and smooth sequential quadratic programming （SQP） method for mathematical programs with nonlinear complementarity constraints （MPCC）. We introduce a class of s...In this paper, we describe a successive approximation and smooth sequential quadratic programming （SQP） method for mathematical programs with nonlinear complementarity constraints （MPCC）. We introduce a class of smooth programs to approximate the MPCC. Using an 11 penalty function, the line search assures global convergence, while the superlinear convergence rate is shown under the strictly complementary and second-order sufficient conditions. Moreover, we prove that the current iterated point is an exact stationary point of the mathematical programs with equilibrium constraints （MPEC） when the algorithm terminates finitely.展开更多
A kind of mathematical programs with equilibrium constraints （MPEC） is studied. By using the idea of successive approximation, a smoothing nonlinear programming, which is equivalent to the MPEC problem, is proposed....A kind of mathematical programs with equilibrium constraints （MPEC） is studied. By using the idea of successive approximation, a smoothing nonlinear programming, which is equivalent to the MPEC problem, is proposed. Thereby, it is ensured that some classical optimization methods can be applied for the MPEC problem. In the end, two algorithm models are proposed with the detail analysis of the global convergence.展开更多
In this paper, by using the notion of convexificator, we introduce the generalized standard Abadie constraint qualification and the generalized MPVC Abadie constraint qualification, and define the generalized stationa...In this paper, by using the notion of convexificator, we introduce the generalized standard Abadie constraint qualification and the generalized MPVC Abadie constraint qualification, and define the generalized stationary conditions for the nonsmooth mathematical program with vanishing constraints (MPVC for short). We show that the generalized strong stationary is the first order necessary optimality condition for nonsmooth MPVC under the generalized standard Abadie constraint qualification. Sufficient conditions for global or local optimality for nonsmooth MPVC are also derived under some generalized convexity assumptions.展开更多
Task scheduling for electro-magnetic detection satellite is a typical combinatorial optimization problem. The count of constraints that need to be taken into account is of large scale. An algorithm combined integer pr...Task scheduling for electro-magnetic detection satellite is a typical combinatorial optimization problem. The count of constraints that need to be taken into account is of large scale. An algorithm combined integer programming with constraint programming is presented. This algorithm is deployed in this problem through two steps. The first step is to decompose the original problem into master and sub-problem using the logic-based Benders decomposition; then a circus combines master and sub-problem solving process together, and the connection between them is general Benders cut. This hybrid algorithm is tested by a set of derived experiments. The result is compared with corresponding outcomes generated by the strength Pareto evolutionary algorithm and the pure constraint programming solver GECODE, which is an open source software. These tests and comparisons yield promising effect.展开更多
An optimal dimension-down iterative algorithm （DDIA） is proposed for solving a mixed （continuous/ discrete） transportation network design problem （MNDP）, which is generally expressed as a mathematical programmin...An optimal dimension-down iterative algorithm （DDIA） is proposed for solving a mixed （continuous/ discrete） transportation network design problem （MNDP）, which is generally expressed as a mathematical programming with equilibrium constraints （MPEC）. The upper level of the MNDP aims to optimize the network performance via both the expansion of existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium （UE） model. The idea of the proposed DDIA is to reduce the dimensions of the problem. A group of variables （discrete/continuous） are fixed to altemately optimize another group of variables （continuous/discrete）. Some continuous network design problems （CNDPs） and discrete network design problems （DNDPs） are solved repeatedly until the optimal solution is obtained. A numerical example is given to demonstrate the efficiency of the proposed algorithm.展开更多
Scheduling a sports tournament is a complex optimization problem,which requires a large number of hard constraints to satisfy.Despite the availability of several such constraints in the literature,there remains a gap ...Scheduling a sports tournament is a complex optimization problem,which requires a large number of hard constraints to satisfy.Despite the availability of several such constraints in the literature,there remains a gap sincemost of the new sports events pose their own unique set of requirements,and demand novel constraints.Specifically talking of the strictly time bound events,ensuring fairness between the different teams in terms of their rest days,traveling,and the number of successive games they play,becomes a difficult task to resolve,and demands attention.In this work,we present a similar situation with a recently played sports event,where a suboptimal schedule favored some of the sides more than the others.We introduce various competitive parameters to draw a fairness comparison between the sides and propose a weighting criterion to point out the sides that enjoyed this schedule more than the others.Furthermore,we use root mean squared error between an ideal schedule and the actual ones for each side to determine unfairness in the distribution of rest days across their entire schedules.The latter is crucial,since successively playing a large number of games may lead to sportsmen burnout,which must be prevented.展开更多
Demand response(DR)using shared energy storage systems(ESSs)is an appealing method to save electricity bills for users under demand charge and time-of-use(TOU)price.A novel Stackelberg-game-based ESS sharing scheme is...Demand response(DR)using shared energy storage systems(ESSs)is an appealing method to save electricity bills for users under demand charge and time-of-use(TOU)price.A novel Stackelberg-game-based ESS sharing scheme is proposed and analyzed in this study.In this scheme,the interactions between selfish users and an operator are characterized as a Stackelberg game.Operator holds a large-scale ESS that is shared among users in the form of energy transactions.It sells energy to users and sets the selling price first.It maximizes its profit through optimal pricing and ESS dispatching.Users purchase some energy from operator for the reduction of their demand charges after operator's selling price is announced.This game-theoretic ESS sharing scheme is characterized and analyzed by formulating and solving a bi-level optimization model.The upper-level optimization maximizes operator's profit and the lower-level optimization minimizes users'costs.The bi-level model is transformed and linearized into a mixed-integer linear programming(MILP)model using the mathematical programming with equilibrium constraints(MPEC)method and model linearizing techniques.Case studies with actual data are carried out to explore the economic performances of the proposed ESS sharing scheme.展开更多
This article discusses feasibility conditions in mathematical programs with equilibrium constraints （MPECs）. The authors prove that two sufficient conditions guarantee the feasibility of these MPECs. The authors sho...This article discusses feasibility conditions in mathematical programs with equilibrium constraints （MPECs）. The authors prove that two sufficient conditions guarantee the feasibility of these MPECs. The authors show that the two feasibility conditions are different from the feasibility condition in [2, 3], and show that the sufficient condition in [3] is stronger than that in [2].展开更多
We focus on second order duality for a class of multiobjective programming problem subject to cone constraints. Four types of second order duality models are formulated. Weak and strong duality theorems are establishe...We focus on second order duality for a class of multiobjective programming problem subject to cone constraints. Four types of second order duality models are formulated. Weak and strong duality theorems are established in terms of the generalized convexity, respectively. Converse duality theorems, essential parts of duality theory, are presented under appropriate assumptions. Moreover, some deficiencies in the work of Ahmad and Agarwal(2010) are discussed.展开更多
In this paper, we study some new systems of generalized quasi-variational inclusion problems in FC-spaces without convexity structure.By applying an existence theorem of maximal elements of set-valued mappings due to ...In this paper, we study some new systems of generalized quasi-variational inclusion problems in FC-spaces without convexity structure.By applying an existence theorem of maximal elements of set-valued mappings due to the author, some new existence theorems of solutions for the systems of generalized quasi-variational inclusion problems are proved in noncompact FC-spaces. As applications, some existence results of solutions for the system of quasi-optimization problems and mathematical programs with the systems of generalized quasi-variational inclusion constraints are obtained in FC-spaces.展开更多
In this paper, we propose a Sample Average Approximation （SAA） method for a class of Stochastic Mathematical Programs with Complementarity Constraints （SMPCC） recently considered by Birbil, G/irkan and Listes [3]....In this paper, we propose a Sample Average Approximation （SAA） method for a class of Stochastic Mathematical Programs with Complementarity Constraints （SMPCC） recently considered by Birbil, G/irkan and Listes [3]. We study the statistical properties of obtained SAA estimators. In particular we show that under moderate conditions a sequence of weak stationary points of SAA programs converge to a weak stationary point of the true problem with probability approaching one at exponential rate as the sample size tends to infinity. To implement the SAA method more efficiently, we incorporate the method with some techniques such as Scholtes＇ regularization method and the well known smoothing NCP method. Some preliminary numerical results are reported.展开更多
In this paper, we present a new trust region algorithm for a nonlinear bilevel programming problem by solving a series of its linear or quadratic approximation subproblems. For the nonlinear bilevel programming proble...In this paper, we present a new trust region algorithm for a nonlinear bilevel programming problem by solving a series of its linear or quadratic approximation subproblems. For the nonlinear bilevel programming problem in which the lower level programming problem is a strongly convex programming problem with linear constraints, we show that each accumulation point of the iterative sequence produced by this algorithm is a stationary point of the bilevel programming problem.展开更多
The command-and-control regulation is likely inefficient and costly.This study investigates a regional pollution control scheme with tax(RPCST)under which the central government sets the tax rate under a given polluta...The command-and-control regulation is likely inefficient and costly.This study investigates a regional pollution control scheme with tax(RPCST)under which the central government sets the tax rate under a given pollutant reduction quota and local governments determine their pollution removal rates based on the central government’s policy.First,a one-leader-multi-follower(OLMF)Stackelberg game model is formulated,in which the central government is the leader and the local governments are the followers.Then,a procedure based on bilevel programming and relaxation method is applied to solve the OLMF model.Finally,a case study analyzing the SO2 reduction of the Yangtze River Delta in China is conducted to demonstrate the effectiveness of the RPCST.The results show that RPCST works better than the current command-andcontrol scheme.Our analysis provides a guideline for governments to design optimal tax schemes to effectively solve the regional air pollution crisis.展开更多
文摘To overcome inefficiency in traditional logic programming, a declarative programming language COPS is designed based on the notion of concurrent constraint programming (CCP). The improvement is achieved by the adoption of constraint-based heuristic strategy and the introduction of deterministic components in the framework of CCP. Syntax specification and an operational semantic description are presented.
文摘This paper addresses the issue of checking consistency in information models. A method based on constraint programming is proposed for identifying inconsistency or proving consistency in information models. The system described here checks information models written in the ISO standard information modelling language EXPRESS. EXPRESS is part of the ISO STEP standard used in the manufacturing and process industries. This paper describes the checking procedure, including EXPRESS model formalization, constraint satisfaction problem (CSP) derivation from the formalized model and satisfaction checking of the derived CSPs. This paper shows a new domain in which constraint programming can be exploited as model verification and validation.
基金Supported in part by NSFC(No.11961011)Guangxi Science and Technology Base and Talents Special Project(No.2021AC06001).
文摘this paper,we propose a class of smoothing-regularization methods for solving the mathematical programming with vanishing constraints.These methods include the smoothing-regularization method proposed by Kanzow et al.in[Comput.Optim.Appl.,2013,55(3):733-767]as a special case.Under the weaker conditions than the ones that have been used by Kanzow et al.in 2013,we prove that the Mangasarian-Fromovitz constraint qualification holds at the feasible points of smoothing-regularization problem.We also analyze that the convergence behavior of the proposed smoothing-regularization method under mild conditions,i.e.,any accumulation point of the stationary point sequence for the smoothing-regularization problem is a strong stationary point.Finally,numerical experiments are given to show the efficiency of the proposed methods.
基金supported by the Funds for the National Natural Science Foundation of China(Nos.52205529 and 62303204)Natural Science Foundation of Shandong Province(Nos.ZR2021QE195 and ZR2021QF036)+2 种基金Youth Innovation Team Program of Shandong Higher Education Institution(No.2023KJ206)Guangyue。Youth Scholar Innovation Talent Program support received from Liaocheng University(No.LCUGYTD2022-03)Foundation of Young Talent of Lifting engineering for Science and Technology in Shandong,China(No.SDAST2024QTA074).
文摘In real production,machines are operated by workers,and the constraints of worker flexibility should be considered.The flexible job shop scheduling problem with both machine and worker resources(DRCFJSP)has become a research hotspot in recent years.In this paper,DRCFJSP with the objective of minimizing the makespan is studied,and it should solve three sub-problems:machine allocation,worker allocation,and operations sequencing.To solve DRCFJSP,a novel hybrid algorithm(CEAM-CP)of cooperative evolutionary algorithm with multiple populations(CEAM)and constraint programming(CP)is proposed.Specifically,the CEAM-CP algorithm is comprised of two main stages.In the first stage,CEAM is used based on three-layer encoding and full active decoding.Moreover,CEAM has three populations,each of which corresponds to one layer encoding and determines one sub-problem.Moreover,each population evolves cooperatively by multiple cross operations.To further improve the solution quality obtained by CEAM,CP is adopted in the second stage.Experiments are conducted on 13 benchmark instances to assess the effectiveness of multiple crossover operations,CP,and CEAM-CP.Most importantly,the proposed CEAM-CP improves 9 best-known solutions out of 13 benchmark instances.
基金supported by the Natural Science Basic Research Plan in Shaanxi Province of China(2013JM1022)the Fundamental Research Funds for the Central Universities(K50511700004)
文摘A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forced to be integer. An integer coding for upper level variables is adopted, and then a discrete differential evolution algorithm with an improved feasibility-based comparison is developed to directly explore the integer solution at the upper level. For a given upper level integer variable, the lower level integer programming problem is solved by the existing branch and bound algorithm to obtain the optimal integer solution at the lower level. In the same framework of the algorithm, two other constraint handling methods, i.e. the penalty function method and the feasibility-based comparison method are also tested. The experimental results demonstrate that the discrete differential evolution algorithm with different constraint handling methods is effective in finding the global optimal integer solutions, but the improved constraint handling method performs better than two compared constraint handling methods.
基金supported by the National Natural Science Foundation of China(No.10861005)the Natural Science Foundation of Guangxi Province (No.0728206)the Innovation Project of Guangxi Graduate Education(No. 2009105950701M29).
文摘Mathematical programs with complementarity constraints(MPCC) is an important subclass of MPEC.It is a natural way to solve MPCC by constructing a suitable approximation of the primal problem.In this paper,we propose a new smoothing method for MPCC by using the aggregation technique.A new SQP algorithm for solving the MPCC problem is presented.At each iteration,the master direction is computed by solving a quadratic program,and the revised direction for avoiding the Maratos effect is generated by an explicit formula.As the non-degeneracy condition holds and the smoothing parameter tends to zero,the proposed SQP algorithm converges globally to an S-stationary point of the MPEC problem,its convergence rate is superlinear.Some preliminary numerical results are reported.
基金supported by the National Natural Science Foundation of China (Nos.10501009,10771040)the Natural Science Foundation of Guangxi Province of China (Nos.0728206,0640001)the China Postdoctoral Science Foundation (No.20070410228)
文摘In this paper, we describe a successive approximation and smooth sequential quadratic programming （SQP） method for mathematical programs with nonlinear complementarity constraints （MPCC）. We introduce a class of smooth programs to approximate the MPCC. Using an 11 penalty function, the line search assures global convergence, while the superlinear convergence rate is shown under the strictly complementary and second-order sufficient conditions. Moreover, we prove that the current iterated point is an exact stationary point of the mathematical programs with equilibrium constraints （MPEC） when the algorithm terminates finitely.
基金project supported by the National Natural Science Foundation of China(Nos.10501009 and 60471039)the Natural Science Foundation of Guangxi Province(No.0728206)
文摘A kind of mathematical programs with equilibrium constraints （MPEC） is studied. By using the idea of successive approximation, a smoothing nonlinear programming, which is equivalent to the MPEC problem, is proposed. Thereby, it is ensured that some classical optimization methods can be applied for the MPEC problem. In the end, two algorithm models are proposed with the detail analysis of the global convergence.
文摘In this paper, by using the notion of convexificator, we introduce the generalized standard Abadie constraint qualification and the generalized MPVC Abadie constraint qualification, and define the generalized stationary conditions for the nonsmooth mathematical program with vanishing constraints (MPVC for short). We show that the generalized strong stationary is the first order necessary optimality condition for nonsmooth MPVC under the generalized standard Abadie constraint qualification. Sufficient conditions for global or local optimality for nonsmooth MPVC are also derived under some generalized convexity assumptions.
基金supported by the National Security Fundamental Research Foundation of China (61361)the National Natural Science Foundation of China (61104180)
文摘Task scheduling for electro-magnetic detection satellite is a typical combinatorial optimization problem. The count of constraints that need to be taken into account is of large scale. An algorithm combined integer programming with constraint programming is presented. This algorithm is deployed in this problem through two steps. The first step is to decompose the original problem into master and sub-problem using the logic-based Benders decomposition; then a circus combines master and sub-problem solving process together, and the connection between them is general Benders cut. This hybrid algorithm is tested by a set of derived experiments. The result is compared with corresponding outcomes generated by the strength Pareto evolutionary algorithm and the pure constraint programming solver GECODE, which is an open source software. These tests and comparisons yield promising effect.
基金The National Natural Science Foundation of China(No. 50908235 )China Postdoctoral Science Foundation (No.201003520)
文摘An optimal dimension-down iterative algorithm （DDIA） is proposed for solving a mixed （continuous/ discrete） transportation network design problem （MNDP）, which is generally expressed as a mathematical programming with equilibrium constraints （MPEC）. The upper level of the MNDP aims to optimize the network performance via both the expansion of existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium （UE） model. The idea of the proposed DDIA is to reduce the dimensions of the problem. A group of variables （discrete/continuous） are fixed to altemately optimize another group of variables （continuous/discrete）. Some continuous network design problems （CNDPs） and discrete network design problems （DNDPs） are solved repeatedly until the optimal solution is obtained. A numerical example is given to demonstrate the efficiency of the proposed algorithm.
基金The authors are grateful to the Deanship of Scientific Research at King Saud University,Saudi Arabia for funding this work through the Vice Deanship of Scientific Research Chairs:Chair of Pervasive and Mobile Computing.
文摘Scheduling a sports tournament is a complex optimization problem,which requires a large number of hard constraints to satisfy.Despite the availability of several such constraints in the literature,there remains a gap sincemost of the new sports events pose their own unique set of requirements,and demand novel constraints.Specifically talking of the strictly time bound events,ensuring fairness between the different teams in terms of their rest days,traveling,and the number of successive games they play,becomes a difficult task to resolve,and demands attention.In this work,we present a similar situation with a recently played sports event,where a suboptimal schedule favored some of the sides more than the others.We introduce various competitive parameters to draw a fairness comparison between the sides and propose a weighting criterion to point out the sides that enjoyed this schedule more than the others.Furthermore,we use root mean squared error between an ideal schedule and the actual ones for each side to determine unfairness in the distribution of rest days across their entire schedules.The latter is crucial,since successively playing a large number of games may lead to sportsmen burnout,which must be prevented.
基金supported by the National Natural Science Foundation of China(U21A20478)Zhejiang Provincial Nature Science Foundation of China(LZ21F030004)Key-Area Research and Development Program of Guangdong Province(2018B010107002)。
文摘Demand response(DR)using shared energy storage systems(ESSs)is an appealing method to save electricity bills for users under demand charge and time-of-use(TOU)price.A novel Stackelberg-game-based ESS sharing scheme is proposed and analyzed in this study.In this scheme,the interactions between selfish users and an operator are characterized as a Stackelberg game.Operator holds a large-scale ESS that is shared among users in the form of energy transactions.It sells energy to users and sets the selling price first.It maximizes its profit through optimal pricing and ESS dispatching.Users purchase some energy from operator for the reduction of their demand charges after operator's selling price is announced.This game-theoretic ESS sharing scheme is characterized and analyzed by formulating and solving a bi-level optimization model.The upper-level optimization maximizes operator's profit and the lower-level optimization minimizes users'costs.The bi-level model is transformed and linearized into a mixed-integer linear programming(MILP)model using the mathematical programming with equilibrium constraints(MPEC)method and model linearizing techniques.Case studies with actual data are carried out to explore the economic performances of the proposed ESS sharing scheme.
基金the National Natural Science Foundation of China(70271019)
文摘This article discusses feasibility conditions in mathematical programs with equilibrium constraints （MPECs）. The authors prove that two sufficient conditions guarantee the feasibility of these MPECs. The authors show that the two feasibility conditions are different from the feasibility condition in [2, 3], and show that the sufficient condition in [3] is stronger than that in [2].
基金supported by National Natural Science Foundation of China (Grant Nos. 11431004, 11271391 and 11201511)the Project of Chongqing Science and Technology Committee (Grant No. cstc2014pt-sy00001)Theoretical Foundation and Application Procedure of Environmental Data Envelopment Analysis Model (Grant No. B-Q22L)
文摘We focus on second order duality for a class of multiobjective programming problem subject to cone constraints. Four types of second order duality models are formulated. Weak and strong duality theorems are established in terms of the generalized convexity, respectively. Converse duality theorems, essential parts of duality theory, are presented under appropriate assumptions. Moreover, some deficiencies in the work of Ahmad and Agarwal(2010) are discussed.
基金supported by the Scientific Research Fun of Sichuan Normal University(09ZDL04)the Sichuan Province Leading Academic Discipline Project(SZD0406)
文摘In this paper, we study some new systems of generalized quasi-variational inclusion problems in FC-spaces without convexity structure.By applying an existence theorem of maximal elements of set-valued mappings due to the author, some new existence theorems of solutions for the systems of generalized quasi-variational inclusion problems are proved in noncompact FC-spaces. As applications, some existence results of solutions for the system of quasi-optimization problems and mathematical programs with the systems of generalized quasi-variational inclusion constraints are obtained in FC-spaces.
文摘In this paper, we propose a Sample Average Approximation （SAA） method for a class of Stochastic Mathematical Programs with Complementarity Constraints （SMPCC） recently considered by Birbil, G/irkan and Listes [3]. We study the statistical properties of obtained SAA estimators. In particular we show that under moderate conditions a sequence of weak stationary points of SAA programs converge to a weak stationary point of the true problem with probability approaching one at exponential rate as the sample size tends to infinity. To implement the SAA method more efficiently, we incorporate the method with some techniques such as Scholtes＇ regularization method and the well known smoothing NCP method. Some preliminary numerical results are reported.
基金Supported by the National Natural Science Foundation of China(No.11171348,11171252 and 71232011)
文摘In this paper, we present a new trust region algorithm for a nonlinear bilevel programming problem by solving a series of its linear or quadratic approximation subproblems. For the nonlinear bilevel programming problem in which the lower level programming problem is a strongly convex programming problem with linear constraints, we show that each accumulation point of the iterative sequence produced by this algorithm is a stationary point of the bilevel programming problem.
基金supported by grants from the National Natural Science Foundation of China[grant numbers 71874108,71373155,72131007]the National Social Science Fund of China[grant numbers 18AZD005,16ZDA048]+1 种基金the Chinese Ministry of Education on the key projects of philosophy and social sciences[grant number 17JZD025]the Natural Science Foundation of Shanghai[grant number 22ZR1415900].
文摘The command-and-control regulation is likely inefficient and costly.This study investigates a regional pollution control scheme with tax(RPCST)under which the central government sets the tax rate under a given pollutant reduction quota and local governments determine their pollution removal rates based on the central government’s policy.First,a one-leader-multi-follower(OLMF)Stackelberg game model is formulated,in which the central government is the leader and the local governments are the followers.Then,a procedure based on bilevel programming and relaxation method is applied to solve the OLMF model.Finally,a case study analyzing the SO2 reduction of the Yangtze River Delta in China is conducted to demonstrate the effectiveness of the RPCST.The results show that RPCST works better than the current command-andcontrol scheme.Our analysis provides a guideline for governments to design optimal tax schemes to effectively solve the regional air pollution crisis.
