This article is concerned with second-order necessary and sufficient optimality conditions for optimal control problems governed by 3-dimensional Navier-Stokes equations. The periodic state constraint is considered.
Energy shortage has become one of themost concerning issues in the world today,and improving energy utilization efficiency is a key area of research for experts and scholars worldwide.Small-diameter heat exchangers of...Energy shortage has become one of themost concerning issues in the world today,and improving energy utilization efficiency is a key area of research for experts and scholars worldwide.Small-diameter heat exchangers offer advantages such as reduced material usage,lower refrigerant charge,and compact structure.However,they also face challenges,including increased refrigerant pressure drop and smaller heat transfer area inside the tubes.This paper combines the advantages and disadvantages of both small and large-diameter tubes and proposes a combined-diameter heat exchanger,consisting of large and small diameters,for use in the indoor units of split-type air conditioners.There are relatively few studies in this area.In this paper,A theoretical and numerical computation method is employed to establish a theoretical-numerical calculation model,and its reliability is verified through experiments.Using this model,the optimal combined diameters and flow path design for a combined-diameter heat exchanger using R32 as the working fluid are derived.The results show that the heat transfer performance of all combined diameter configurations improves by 2.79%to 8.26%compared to the baseline design,with the coefficient of performance(COP)increasing from 4.15 to 4.27~4.5.These designs can save copper material,but at the cost of an increase in pressure drop by 66.86%to 131.84%.The scheme IIIH,using R32,is the optimal combined-diameter and flow path configuration that balances both heat transfer performance and economic cost.展开更多
In this paper,we propose and analyze two second-order accurate finite difference schemes for the one-dimensional heat equation with concentrated capacity on a computa-tional domain=[a,b].We first transform the target ...In this paper,we propose and analyze two second-order accurate finite difference schemes for the one-dimensional heat equation with concentrated capacity on a computa-tional domain=[a,b].We first transform the target equation into the standard heat equation on the domain excluding the singular point equipped with an inner interface matching(IIM)condition on the singular point x=ξ∈(a,b),then adopt Taylor’s ex-pansion to approximate the IIM condition at the singular point and apply second-order finite difference method to approximate the standard heat equation at the nonsingular points.This discrete procedure allows us to choose different grid sizes to partition the two sub-domains[a,ξ]and[ξ,b],which ensures that x=ξ is a grid point,and hence the pro-posed schemes can be generalized to the heat equation with more than one concentrated capacities.We prove that the two proposed schemes are uniquely solvable.And through in-depth analysis of the local truncation errors,we rigorously prove that the two schemes are second-order accurate both in temporal and spatial directions in the maximum norm without any constraint on the grid ratio.Numerical experiments are carried out to verify our theoretical conclusions.展开更多
This paper deals with extensions of higher-order optimality conditions for scalar optimization to multiobjective optimization.A type of directional derivatives for a multiobjective function is proposed,and with this n...This paper deals with extensions of higher-order optimality conditions for scalar optimization to multiobjective optimization.A type of directional derivatives for a multiobjective function is proposed,and with this notion characterizations of strict local minima of order k for a multiobjective optimization problem with a nonempty set constraint are established,generalizing the corresponding scalar case obtained by Studniarski[3].Also necessary not sufficient and sufficient not necessary optimality conditions for this minima are derived based on our directional derivatives,which are generalizations of some existing scalar results and equivalent to some existing multiobjective ones.Many examples are given to illustrate them there.展开更多
In this paper, we establish a second-order sufficient condition for constrained optimization problems of a class of so called t-stable functions in terms of the first-order and the second-order Dini type directional d...In this paper, we establish a second-order sufficient condition for constrained optimization problems of a class of so called t-stable functions in terms of the first-order and the second-order Dini type directional derivatives. The result extends the corresponding result of [D. Bednarik and K. Pastor, Math. Program. Ser. A, 113（2008）, 283-298] to constrained optimization problems.展开更多
In this paper,we investigate the multi-objective optimal control problem of ordinary differential equations on Riemannian manifolds.We first obtain the second-order necessary conditions for weak Pareto optimal solutio...In this paper,we investigate the multi-objective optimal control problem of ordinary differential equations on Riemannian manifolds.We first obtain the second-order necessary conditions for weak Pareto optimal solutions for multi-objective optimal control problems with fixed terminal time,and then extend these results to multi-objective optimal control problems with free terminal time,deriving the corresponding second-order necessary conditions for weak Pareto optimal solutions.Our main results show that weak Pareto optimal solutions depend on the curvature tensor of the Riemannian manifold.Finally,we provide an example as an application of our main results,illustrating how our findings differ from existing related results.展开更多
Bifunctional oxide-zeolite-based composites(OXZEO)have emerged as promising materials for the direct conversion of syngas to olefins.However,experimental screening and optimization of reaction parameters remain resour...Bifunctional oxide-zeolite-based composites(OXZEO)have emerged as promising materials for the direct conversion of syngas to olefins.However,experimental screening and optimization of reaction parameters remain resource-intensive.To address this challenge,we implemented a three-stage framework integrating machine learning,Bayesian optimization,and experimental validation,utilizing a carefully curated dataset from the literature.Our ensemble-tree model(R^(2)>0.87)identified Zn-Zr and Cu-Mg binary mixed oxides as the most effective OXZEO systems,with their light olefin space-time yields confirmed by physically mixing with HSAPO-34 through experimental validation.Density functional theory calculations further elucidated the activity trends between Zn-Zr and Cu-Mg mixed oxides.Among 16 catalyst and reaction condition descriptors,the oxide/zeolite ratio,reaction temperature,and pressure emerged as the most significant factors.This interpretable,data-driven framework offers a versatile approach that can be applied to other catalytic processes,providing a powerful tool for experiment design and optimization in catalysis.展开更多
As future ship system,hybrid energy ship system has a wide range of application prospects for solving the serious energy crisis.However,current optimization scheduling works lack the consideration of sea conditions an...As future ship system,hybrid energy ship system has a wide range of application prospects for solving the serious energy crisis.However,current optimization scheduling works lack the consideration of sea conditions and navigational circumstances.There-fore,this paper aims at establishing a two-stage optimization framework for hybrid energy ship power system.The proposed framework considers multiple optimizations of route,speed planning,and energy management under the constraints of sea conditions during navigation.First,a complex hybrid ship power model consisting of diesel generation system,propulsion system,energy storage system,photovoltaic power generation system,and electric boiler system is established,where sea state information and ship resistance model are considered.With objective optimization functions of cost and greenhouse gas(GHG)emissions,a two-stage optimization framework consisting of route planning,speed scheduling,and energy management is constructed.Wherein the improved A-star algorithm and grey wolf optimization algorithm are introduced to obtain the optimal solutions for route,speed,and energy optimization scheduling.Finally,simulation cases are employed to verify that the proposed two-stage optimization scheduling model can reduce load energy consumption,operating costs,and carbon emissions by 17.8%,17.39%,and 13.04%,respectively,compared with the non-optimal control group.展开更多
The Conditional Nonlinear Optimal Perturbation(CNOP)method works essentially for conventional numerical models;however,it is not fully applicable to the commonly used deep-learning forecasting models(DLMs),which typic...The Conditional Nonlinear Optimal Perturbation(CNOP)method works essentially for conventional numerical models;however,it is not fully applicable to the commonly used deep-learning forecasting models(DLMs),which typically input multiple time slices without deterministic dependencies.In this study,the CNOP for DLMs(CNOP-DL)is proposed as an extension of the CNOP in the time dimension.This method is useful for targeted observations as it indicates not only where but also when to deploy additional observations.The CNOP-DL is calculated for a forecast case of sea surface temperature in the South China Sea with a DLM.The CNOP-DL identifies a sensitive area northwest of Palawan Island at the last input time.Sensitivity experiments demonstrate that the sensitive area identified by the CNOP-DL is effective not only for the CNOP-DL itself,but also for random perturbations.Therefore,this approach holds potential for guiding practical field campaigns.Notably,forecast errors are more sensitive to time than to location in the sensitive area.It highlights the crucial role of identifying the time of the sensitive area in targeted observations,corroborating the usefulness of extending the CNOP in the time dimension.展开更多
Machinery condition monitoring is beneficial to equipment maintenance and has been receiving much attention from academia and industry.Machine learning,especially deep learning,has become popular for machinery conditi...Machinery condition monitoring is beneficial to equipment maintenance and has been receiving much attention from academia and industry.Machine learning,especially deep learning,has become popular for machinery condition monitoring because that can fully use available data and computational power.Since significant accidents might be caused if wrong fault alarms are given for machine condition monitoring,interpretable machine learning models,integrate signal processing knowledge to enhance trustworthiness of models,are gradually becoming a research hotspot.A previous spectrum-based and interpretable optimized weights method has been proposed to indicate faulty and fundamental frequencies when the analyzed data only contains a healthy type and a fault type.Considering that multiclass fault types are naturally met in practice,this work aims to explore the interpretable optimized weights method for multiclass fault type scenarios.Therefore,a new multiclass optimized weights spectrum(OWS)is proposed and further studied theoretically and numerically.It is found that the multiclass OWS is capable of capturing the characteristic components associated with different conditions and clearly indicating specific fault characteristic frequencies(FCFs)corresponding to each fault condition.This work can provide new insights into spectrum-based fault classification models,and the new multiclass OWS also shows great potential for practical applications.展开更多
In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a （weakly） LU-efficient solution in the considered nonsmooth multiobjective programming problem with the mult...In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a （weakly） LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a （weakly） LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval- objective function are convex.展开更多
The concepts of alpha-order Clarke's derivative, alpha-order Adjacent derivative and alpha-order G.Bouligand derivative of set-valued mappings are introduced, their properties are studied, with which the Fritz Joh...The concepts of alpha-order Clarke's derivative, alpha-order Adjacent derivative and alpha-order G.Bouligand derivative of set-valued mappings are introduced, their properties are studied, with which the Fritz John optimality condition of set-valued vector optimization is established. Finally, under the assumption of pseudoconvexity, the optimality condition is proved to be sufficient.展开更多
New classes of functions namely (V, ρ)_(h,φ)-type I, quasi (V, ρ)_(h,φ)-type I and pseudo (V, ρ)_(h,φ)-type I functions are defined for multiobjective programming problem by using BenTal's generalized algebr...New classes of functions namely (V, ρ)_(h,φ)-type I, quasi (V, ρ)_(h,φ)-type I and pseudo (V, ρ)_(h,φ)-type I functions are defined for multiobjective programming problem by using BenTal's generalized algebraic operation. The examples of (V, ρ)_(h,φ)-type I functions are given. The sufficient optimality conditions are obtained for multi-objective programming problem involving above new generalized convexity.展开更多
Quadratic 0-1 problems with linear inequality constraints are briefly considered in this paper.Global optimality conditions for these problems,including a necessary condition and some sufficient conditions,are present...Quadratic 0-1 problems with linear inequality constraints are briefly considered in this paper.Global optimality conditions for these problems,including a necessary condition and some sufficient conditions,are presented.The necessary condition is expressed without dual variables.The relations between the global optimal solutions of nonconvex quadratic 0-1 problems and the associated relaxed convex problems are also studied.展开更多
This paper studies a class of multiobjective generalized fractional programming problems, where the numerators of objective functions are the sum of differentiable function and convex function, while the denominators ...This paper studies a class of multiobjective generalized fractional programming problems, where the numerators of objective functions are the sum of differentiable function and convex function, while the denominators are the difference of differentiable function and convex function. Under the assumption of Calmness Constraint Qualification the Kuhn-Tucker type necessary conditions for efficient solution are given, and the Kuhn-Tucker type sufficient conditions for efficient solution are presented under the assumptions of （F, α, ρ, d）-V-convexity. Subsequently, the optimality conditions for two kinds of duality models are formulated and duality theorems are proved.展开更多
In this paper, we introduce generalized essentially pseudoconvex function and generalized essentially quasiconvex function, and give sufficient optimality conditions of the nonsmooth generalized convex multi-objective...In this paper, we introduce generalized essentially pseudoconvex function and generalized essentially quasiconvex function, and give sufficient optimality conditions of the nonsmooth generalized convex multi-objective programming and its saddle point theorem about cone efficient solution. We set up Mond-Weir type duality and Craven type duality for nonsmooth multiobjective programming with generalized essentially convex functions, and prove them.展开更多
In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These co...In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These conditions are responsible for the development of duality theory which is an extremely important feature for any class of problems, but the literature available so far lacks these necessary optimality conditions for the stated problem. A lemma is also proved to find the topological dual of as it is required to prove the desired result.展开更多
There are two approaches of defining the solutions of a set-valued optimization problem： vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions...There are two approaches of defining the solutions of a set-valued optimization problem： vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives. In the case of vector criterion, some optimality conditions are derived for isolated （weak） minimizers. With set criterion, necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation.展开更多
In this paper, new sufficient optimality theorems for a solution of a differentiable bilevel multiobjective optimization problem (BMOP) are established. We start with a discussion on solution concepts in bilevel multi...In this paper, new sufficient optimality theorems for a solution of a differentiable bilevel multiobjective optimization problem (BMOP) are established. We start with a discussion on solution concepts in bilevel multiobjective programming;a theorem giving necessary and sufficient conditions for a decision vector to be called a solution of the BMOP and a proposition giving the relations between four types of solutions of a BMOP are presented and proved. Then, under the pseudoconvexity assumptions on the upper and lower level objective functions and the quasiconvexity assumptions on the constraints functions, we establish and prove two new sufficient optimality theorems for a solution of a general BMOP with coupled upper level constraints. Two corollary of these theorems, in the case where the upper and lower level objectives and constraints functions are convex are presented.展开更多
This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for...This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for Henig effcient solutions of set-valued optimization problems whose constraint condition is determined by a fixed set.展开更多
基金This work was supported by National Natural Science Foundation of China (10401041)Natural Science Foundation of Hubei Province (2004ABA009)
文摘This article is concerned with second-order necessary and sufficient optimality conditions for optimal control problems governed by 3-dimensional Navier-Stokes equations. The periodic state constraint is considered.
基金supported by Supported by the Scientific Research Foundation for High-Level Talents of Zhoukou Normal University(ZKNUC2024018).
文摘Energy shortage has become one of themost concerning issues in the world today,and improving energy utilization efficiency is a key area of research for experts and scholars worldwide.Small-diameter heat exchangers offer advantages such as reduced material usage,lower refrigerant charge,and compact structure.However,they also face challenges,including increased refrigerant pressure drop and smaller heat transfer area inside the tubes.This paper combines the advantages and disadvantages of both small and large-diameter tubes and proposes a combined-diameter heat exchanger,consisting of large and small diameters,for use in the indoor units of split-type air conditioners.There are relatively few studies in this area.In this paper,A theoretical and numerical computation method is employed to establish a theoretical-numerical calculation model,and its reliability is verified through experiments.Using this model,the optimal combined diameters and flow path design for a combined-diameter heat exchanger using R32 as the working fluid are derived.The results show that the heat transfer performance of all combined diameter configurations improves by 2.79%to 8.26%compared to the baseline design,with the coefficient of performance(COP)increasing from 4.15 to 4.27~4.5.These designs can save copper material,but at the cost of an increase in pressure drop by 66.86%to 131.84%.The scheme IIIH,using R32,is the optimal combined-diameter and flow path configuration that balances both heat transfer performance and economic cost.
基金supported by the National Natural Science Foundation of China(Grant No.11571181)by the Natural Science Foundation of Jiangsu Province(Grant No.BK20171454).
文摘In this paper,we propose and analyze two second-order accurate finite difference schemes for the one-dimensional heat equation with concentrated capacity on a computa-tional domain=[a,b].We first transform the target equation into the standard heat equation on the domain excluding the singular point equipped with an inner interface matching(IIM)condition on the singular point x=ξ∈(a,b),then adopt Taylor’s ex-pansion to approximate the IIM condition at the singular point and apply second-order finite difference method to approximate the standard heat equation at the nonsingular points.This discrete procedure allows us to choose different grid sizes to partition the two sub-domains[a,ξ]and[ξ,b],which ensures that x=ξ is a grid point,and hence the pro-posed schemes can be generalized to the heat equation with more than one concentrated capacities.We prove that the two proposed schemes are uniquely solvable.And through in-depth analysis of the local truncation errors,we rigorously prove that the two schemes are second-order accurate both in temporal and spatial directions in the maximum norm without any constraint on the grid ratio.Numerical experiments are carried out to verify our theoretical conclusions.
文摘This paper deals with extensions of higher-order optimality conditions for scalar optimization to multiobjective optimization.A type of directional derivatives for a multiobjective function is proposed,and with this notion characterizations of strict local minima of order k for a multiobjective optimization problem with a nonempty set constraint are established,generalizing the corresponding scalar case obtained by Studniarski[3].Also necessary not sufficient and sufficient not necessary optimality conditions for this minima are derived based on our directional derivatives,which are generalizations of some existing scalar results and equivalent to some existing multiobjective ones.Many examples are given to illustrate them there.
基金The Graduate Students Innovate Scientific Research Program (YJSCX2008-158HLJ) of Heilongjiang Provincesupported by the Distinguished Young Scholar Foundation (JC200707) of Heilongjiang Province of China
文摘In this paper, we establish a second-order sufficient condition for constrained optimization problems of a class of so called t-stable functions in terms of the first-order and the second-order Dini type directional derivatives. The result extends the corresponding result of [D. Bednarik and K. Pastor, Math. Program. Ser. A, 113（2008）, 283-298] to constrained optimization problems.
基金supported by National Natural Science Foundation of China(Grant No.12371451)Natural Science Foundation of Sichuan Province(Grant No.2025ZNSFSC0077)。
文摘In this paper,we investigate the multi-objective optimal control problem of ordinary differential equations on Riemannian manifolds.We first obtain the second-order necessary conditions for weak Pareto optimal solutions for multi-objective optimal control problems with fixed terminal time,and then extend these results to multi-objective optimal control problems with free terminal time,deriving the corresponding second-order necessary conditions for weak Pareto optimal solutions.Our main results show that weak Pareto optimal solutions depend on the curvature tensor of the Riemannian manifold.Finally,we provide an example as an application of our main results,illustrating how our findings differ from existing related results.
基金funded by the KRICT Project (KK2512-10) of the Korea Research Institute of Chemical Technology and the Ministry of Trade, Industry and Energy (MOTIE)the Korea Institute for Advancement of Technology (KIAT) through the Virtual Engineering Platform Program (P0022334)+1 种基金supported by the Carbon Neutral Industrial Strategic Technology Development Program (RS-202300261088) funded by the Ministry of Trade, Industry & Energy (MOTIE, Korea)Further support was provided by research fund of Chungnam National University。
文摘Bifunctional oxide-zeolite-based composites(OXZEO)have emerged as promising materials for the direct conversion of syngas to olefins.However,experimental screening and optimization of reaction parameters remain resource-intensive.To address this challenge,we implemented a three-stage framework integrating machine learning,Bayesian optimization,and experimental validation,utilizing a carefully curated dataset from the literature.Our ensemble-tree model(R^(2)>0.87)identified Zn-Zr and Cu-Mg binary mixed oxides as the most effective OXZEO systems,with their light olefin space-time yields confirmed by physically mixing with HSAPO-34 through experimental validation.Density functional theory calculations further elucidated the activity trends between Zn-Zr and Cu-Mg mixed oxides.Among 16 catalyst and reaction condition descriptors,the oxide/zeolite ratio,reaction temperature,and pressure emerged as the most significant factors.This interpretable,data-driven framework offers a versatile approach that can be applied to other catalytic processes,providing a powerful tool for experiment design and optimization in catalysis.
基金supported by the National Natural Science Foundation of China under Grant 62473328by the Open Research Fund of Jiangsu Collaborative Innovation Center for Smart Distribution Network,Nanjing Institute of Technology under No.XTCX202203.
文摘As future ship system,hybrid energy ship system has a wide range of application prospects for solving the serious energy crisis.However,current optimization scheduling works lack the consideration of sea conditions and navigational circumstances.There-fore,this paper aims at establishing a two-stage optimization framework for hybrid energy ship power system.The proposed framework considers multiple optimizations of route,speed planning,and energy management under the constraints of sea conditions during navigation.First,a complex hybrid ship power model consisting of diesel generation system,propulsion system,energy storage system,photovoltaic power generation system,and electric boiler system is established,where sea state information and ship resistance model are considered.With objective optimization functions of cost and greenhouse gas(GHG)emissions,a two-stage optimization framework consisting of route planning,speed scheduling,and energy management is constructed.Wherein the improved A-star algorithm and grey wolf optimization algorithm are introduced to obtain the optimal solutions for route,speed,and energy optimization scheduling.Finally,simulation cases are employed to verify that the proposed two-stage optimization scheduling model can reduce load energy consumption,operating costs,and carbon emissions by 17.8%,17.39%,and 13.04%,respectively,compared with the non-optimal control group.
基金supported by the National Natural Science Foundation of China (Grant No. 42288101, 42375062, 42476192, 42275158)the National Key Scientific and Technological Infrastructure project “Earth System Science Numerical Simulator Facility” (Earth Lab)the GHfund C (202407036001)
文摘The Conditional Nonlinear Optimal Perturbation(CNOP)method works essentially for conventional numerical models;however,it is not fully applicable to the commonly used deep-learning forecasting models(DLMs),which typically input multiple time slices without deterministic dependencies.In this study,the CNOP for DLMs(CNOP-DL)is proposed as an extension of the CNOP in the time dimension.This method is useful for targeted observations as it indicates not only where but also when to deploy additional observations.The CNOP-DL is calculated for a forecast case of sea surface temperature in the South China Sea with a DLM.The CNOP-DL identifies a sensitive area northwest of Palawan Island at the last input time.Sensitivity experiments demonstrate that the sensitive area identified by the CNOP-DL is effective not only for the CNOP-DL itself,but also for random perturbations.Therefore,this approach holds potential for guiding practical field campaigns.Notably,forecast errors are more sensitive to time than to location in the sensitive area.It highlights the crucial role of identifying the time of the sensitive area in targeted observations,corroborating the usefulness of extending the CNOP in the time dimension.
基金supported by the National Natural Science Foundation of China under Grant Nos.523B2043 and 52475112.
文摘Machinery condition monitoring is beneficial to equipment maintenance and has been receiving much attention from academia and industry.Machine learning,especially deep learning,has become popular for machinery condition monitoring because that can fully use available data and computational power.Since significant accidents might be caused if wrong fault alarms are given for machine condition monitoring,interpretable machine learning models,integrate signal processing knowledge to enhance trustworthiness of models,are gradually becoming a research hotspot.A previous spectrum-based and interpretable optimized weights method has been proposed to indicate faulty and fundamental frequencies when the analyzed data only contains a healthy type and a fault type.Considering that multiclass fault types are naturally met in practice,this work aims to explore the interpretable optimized weights method for multiclass fault type scenarios.Therefore,a new multiclass optimized weights spectrum(OWS)is proposed and further studied theoretically and numerically.It is found that the multiclass OWS is capable of capturing the characteristic components associated with different conditions and clearly indicating specific fault characteristic frequencies(FCFs)corresponding to each fault condition.This work can provide new insights into spectrum-based fault classification models,and the new multiclass OWS also shows great potential for practical applications.
文摘In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a （weakly） LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a （weakly） LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval- objective function are convex.
基金the National Natural Science Foundation(69972036) and the Natural Science Foundation of Shanxi province(995L02)
文摘The concepts of alpha-order Clarke's derivative, alpha-order Adjacent derivative and alpha-order G.Bouligand derivative of set-valued mappings are introduced, their properties are studied, with which the Fritz John optimality condition of set-valued vector optimization is established. Finally, under the assumption of pseudoconvexity, the optimality condition is proved to be sufficient.
基金Supported by the NSF of Shaanxi Provincial Educational Department(06JK152)
文摘New classes of functions namely (V, ρ)_(h,φ)-type I, quasi (V, ρ)_(h,φ)-type I and pseudo (V, ρ)_(h,φ)-type I functions are defined for multiobjective programming problem by using BenTal's generalized algebraic operation. The examples of (V, ρ)_(h,φ)-type I functions are given. The sufficient optimality conditions are obtained for multi-objective programming problem involving above new generalized convexity.
文摘Quadratic 0-1 problems with linear inequality constraints are briefly considered in this paper.Global optimality conditions for these problems,including a necessary condition and some sufficient conditions,are presented.The necessary condition is expressed without dual variables.The relations between the global optimal solutions of nonconvex quadratic 0-1 problems and the associated relaxed convex problems are also studied.
基金Supported by Chongqing Key Lab. of Operations Research and System Engineering
文摘This paper studies a class of multiobjective generalized fractional programming problems, where the numerators of objective functions are the sum of differentiable function and convex function, while the denominators are the difference of differentiable function and convex function. Under the assumption of Calmness Constraint Qualification the Kuhn-Tucker type necessary conditions for efficient solution are given, and the Kuhn-Tucker type sufficient conditions for efficient solution are presented under the assumptions of （F, α, ρ, d）-V-convexity. Subsequently, the optimality conditions for two kinds of duality models are formulated and duality theorems are proved.
文摘In this paper, we introduce generalized essentially pseudoconvex function and generalized essentially quasiconvex function, and give sufficient optimality conditions of the nonsmooth generalized convex multi-objective programming and its saddle point theorem about cone efficient solution. We set up Mond-Weir type duality and Craven type duality for nonsmooth multiobjective programming with generalized essentially convex functions, and prove them.
文摘In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These conditions are responsible for the development of duality theory which is an extremely important feature for any class of problems, but the literature available so far lacks these necessary optimality conditions for the stated problem. A lemma is also proved to find the topological dual of as it is required to prove the desired result.
基金Supported by the National Natural Science Foundation of China(11361001)Natural Science Foundation of Ningxia(NZ14101)
文摘There are two approaches of defining the solutions of a set-valued optimization problem： vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives. In the case of vector criterion, some optimality conditions are derived for isolated （weak） minimizers. With set criterion, necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation.
文摘In this paper, new sufficient optimality theorems for a solution of a differentiable bilevel multiobjective optimization problem (BMOP) are established. We start with a discussion on solution concepts in bilevel multiobjective programming;a theorem giving necessary and sufficient conditions for a decision vector to be called a solution of the BMOP and a proposition giving the relations between four types of solutions of a BMOP are presented and proved. Then, under the pseudoconvexity assumptions on the upper and lower level objective functions and the quasiconvexity assumptions on the constraints functions, we establish and prove two new sufficient optimality theorems for a solution of a general BMOP with coupled upper level constraints. Two corollary of these theorems, in the case where the upper and lower level objectives and constraints functions are convex are presented.
基金Supported by the National Natural Science Foundation of China（10871216） Supported by the Science and Technology Research Project of Chongqing Municipal Education Commission（KJ100419） Supported by the Natural Science Foundation Project of CQ CSTC（cstcjjA00019）
文摘This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for Henig effcient solutions of set-valued optimization problems whose constraint condition is determined by a fixed set.
