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Optimality conditions and duality for a class of nondifferentiable multiobjective generalized fractional programming problems 认领 引用 被引量：1
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作者 GAO Ying RONG Wei-dong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE 2008年第3期331-344,共14页
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 ar... 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
关键词 operations research multiobjective generalized fractional programming optimality condition duality theorem generalized convexity
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Connectedness of Cone-efficient Solution Set for Cone-quasiconvex Multiobjective Programming in Hausdorff Topological Vector Spaces 认领 引用 被引量：2
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作者 ZHOU Xuan-wei 《Chinese Quarterly Journal of Mathematics》 2010年第1期132-139,共8页
This paper deals with the connectedness of the cone-efficient solution set for vector optimization in locally convex Hausdorff topological vector spaces. The connectedness of the cone-efficient solution set is proved ... This paper deals with the connectedness of the cone-efficient solution set for vector optimization in locally convex Hausdorff topological vector spaces. The connectedness of the cone-efficient solution set is proved for multiobjective programming defined by a continuous one-to-one cone-quasiconvex mapping on a compact convex set of alternatives. During the proof, the generalized saddle theorem plays a key role. 展开更多
关键词 multiobjective programming cone-efficient solution cone-quasiconvex mapping generalized saddle theorem connectedness
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Duality Relations for a Class of a Multiobjective Fractional Programming Problem Involving Support Functions 认领 引用
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作者   Vandana Ramu Dubey +2 位作者   Deepmala Lakshmi Narayan Mishra Vishnu Narayan Mishra 《American Journal of Operations Research》 2018年第4期294-311,共18页
In this article, for a differentiable function , we introduce the definition of the higher-order -invexity. Three duality models for a multiobjective fractional programming problem involving nondifferentiability in te... In this article, for a differentiable function , we introduce the definition of the higher-order -invexity. Three duality models for a multiobjective fractional programming problem involving nondifferentiability in terms of support functions have been formulated and usual duality relations have been established under the higher-order -invex assumptions. 展开更多
关键词 Efficient Solution Support Function Multiobjective Fractional Programming Generalized Invexity
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Sufficiency and Duality for Nondif ferentiable Multiobjective Fractional Programming Problems with (Φ,ρ,α)-V-Invexity 认领 引用 被引量：2
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作者 闫春雷 杨舒先 《Journal of Donghua University(English Edition)》 CAS 2017年第2期178-183,共6页
A new concept of(Φ,ρ,α)-V-invexity for differentiable vector-valued functions is introduced,which is a generalization of differentiable scalar-valued(Φ,ρ)-invexity.Based upon the(Φ,ρ,α)-V-invex functions,suffi... A new concept of(Φ,ρ,α)-V-invexity for differentiable vector-valued functions is introduced,which is a generalization of differentiable scalar-valued(Φ,ρ)-invexity.Based upon the(Φ,ρ,α)-V-invex functions,sufficient optimality conditions and MondWeir type dual theorems are derived for a class of nondifferentiable multiobjective fractional programming problems in which every component of the objective function and each constraint function contain a term involving the support function of a compact convex set. 展开更多
关键词 nondifferentiable multiobjective fractional programming efficiency (Φ,ρ,α)-V-invexity sufficiency duality
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Necessary and Sufficient Conditions in Smooth Programming with Generalized Convexity 认领 引用 被引量：5
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作者 孙清滢 叶留青 《Chinese Quarterly Journal of Mathematics》 2000年第4期33-37,共5页
Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded un... Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded univex functions, a new class of functions that unifies several concepts of generalized convexity. In this paper, additional conditions are attached to the Kuhn Tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization, under appropriate constraint qualifications. 展开更多
关键词 necessary and sufficient conditions generalized convexity nonlinear programming multiobjective programming type Ⅰ functions
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MAJOR-EFFICIENT SOLUTIONS AND WEAKLY MAJOR-EFFICIENT SOLUTIONS OF MULTIOBJECTIVE PROGRAMMING 认领 引用 被引量：15
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作者 HU YUDA 《Applied Mathematics(A Journal of Chinese Universities)》 1994年第1期85-94,共10页
In this papert the theory of major efficiency for multiobjective programmingis established.The major-efficient solutions and weakly major-efficient solutions of multiobjective programming given here are Pareto efficie... In this papert the theory of major efficiency for multiobjective programmingis established.The major-efficient solutions and weakly major-efficient solutions of multiobjective programming given here are Pareto efficient solutions of the same multiobjectiveprogramming problem, but the converse is not true. In a ceratin sense , these solutionsare in fact better than any other Pareto efficient solutions. Some basic theorems whichcharacterize major-efficient solutions and weakly major-efficient solutions of multiobjective programming are stated and proved. Furthermore,the existence and some geometricproperties of these solutions are studied. 展开更多
关键词 Multiobjective Programming Pareto Efficient Solution Major-EfficientSolution Weakly Major-Efficient Solution.
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Optimality Conditions and Duality for Nonsmooth Multiobjective Programms with Generalized Essential Convexity 认领 引用 被引量：1
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作者 王彩玲 刘庆怀 李忠范 《Northeastern Mathematical Journal》 2008年第5期377-385,共9页
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
关键词 multiobjective programming optimality condition saddle point duality
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Duality for Dini-Invex Nonsmooth Multiobjective Programming 认领 引用
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作者 李忠范 刘庆怀 杨荣 《Northeastern Mathematical Journal》 2005年第3期265-270,共6页
In this paper we generalize the concept of a Dini-convex function with Dini derivative and introduce a new concept - Dini-invexity. Some properties of Diniinvex functions are discussed. On the base of this, we study t... In this paper we generalize the concept of a Dini-convex function with Dini derivative and introduce a new concept - Dini-invexity. Some properties of Diniinvex functions are discussed. On the base of this, we study the Wolfe type duality and Mond-Weir type duality for Dini-invex nonsmooth multiobjective programmings and obtain corresponding duality theorems. 展开更多
关键词 Dini-invexity nonsmooth multiobjective programming duality
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Nondifferentiable Multiobjective Programming under Generalized d_I-G-Type I Invexity 认领 引用
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作者 闫春雷 《Journal of Donghua University(English Edition)》 EI CAS 2013年第4期293-297,共5页
To relax convexity assumptions imposed on the functions in theorems on sufficient conditions and duality,new concepts of generalized dI-G-type Ⅰ invexity were introduced for nondifferentiable multiobjective programmi... To relax convexity assumptions imposed on the functions in theorems on sufficient conditions and duality,new concepts of generalized dI-G-type Ⅰ invexity were introduced for nondifferentiable multiobjective programming problems.Based upon these generalized invexity,G-Fritz-John （G-F-J） and G-Karnsh-Kuhn-Tucker （G-K-K-T） types sufficient optimality conditions were established for a feasible solution to be an efficient solution.Moreover,weak and strict duality results were derived for a G-Mond-Weir type dual under various types of generalized dI-G-type Ⅰ invexity assumptions. 展开更多
关键词 nondifferentiable multiobjective program efficient solution generalized dI-G-type Ⅰ invexity sufficient optimality conditions dualityCLC number：O221.6Document code：AArticle ID：1672-5220（2013）04-0293-05
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THE SUFFICIENT EFFICIENCY CONDITIONS IN SEMIINFINITE MULTIOBJECTIVE FRACTIONAL PROGRAMMING UNDER HIGHER ORDER EXPONENTIAL TYPE HYBRID TYPE INVEXITIES 认领 引用
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作者 Ram U.VERMA 《Acta Mathematica Scientia》 SCIE CSCD 2015年第6期1437-1453,共17页
First, a class of higher order exponential type hybrid （α,β, γ, η, p, h（.,.）, κ（., .）, w（.,., .）, ω（.,.,.）, θ）-invexities is introduced, second, some parametrically sufficient efficiency conditions ba... First, a class of higher order exponential type hybrid （α,β, γ, η, p, h（.,.）, κ（., .）, w（.,., .）, ω（.,.,.）, θ）-invexities is introduced, second, some parametrically sufficient efficiency conditions based on the higher order exponential type hybrid invexities are established, and finally some parametrically sufficient efficiency results under the higher order exponential type hybrid （a,β, γ, ρ, h（.,.）, k（.,-）, w（-,., .）, w（.,., .）, 0）-invexities are investigated to the context of solving semiinfinite multiobjective fractional programming problems. The notions of the higher order exponential type hybrid （a, β, γ η, p, h（., .）, n（., .）, w（-,.,-）, ω（.,.,.）, 0）-invexities encompass most of the generalized invexities in the literature. To the best of our knowledge, the results on semiinfinite multiobjective fractional programming problems established in this communication are new and application-oriented toward multitime multi- objectve problems as well as multiobiective control problems. 展开更多
关键词 semiinfinite fractional programming multiobjective fractional programming,Hanson-Antczak-type generalized HAα,β,γ,η,ρh-V-invex functions hy-（α,β,γ,η,ρh（.,.）,k（.,.）,w（.,.,.）w（.,.,.）,θ-invexity）
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Duality for Multiobjective Bilevel Programming Problems with Extremal-Value Function 认领 引用 被引量：1
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作者 Haijun WANG Ruifang ZHANG 《Journal of Mathematical Research with Applications》 CSCD 2015年第3期311-320,共10页
For a multiobjective bilevel programnfing problem （P） with an extremal-value function, its dual problem is constructed by using the Fenchel-Moreau conjugate of the functions involved. Under some convexity and monoto... For a multiobjective bilevel programnfing problem （P） with an extremal-value function, its dual problem is constructed by using the Fenchel-Moreau conjugate of the functions involved. Under some convexity and monotonicity assumptions, the weak and strong duality assertions are obtained. 展开更多
关键词 multiobjective optimization bilevel programming problems conjugate duality convex programming composed convex functions
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Chance-Constrained Approaches for Multiobjective Stochastic Linear Programming Problems 认领 引用 被引量：2
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作者 Justin Dupar Busili Kampempe Monga Kalonda Luhandjula 《American Journal of Operations Research》 2012年第4期519-526,共8页
Multiple objective stochastic linear programming is a relevant topic. As a matter of fact, many practical problems ranging from portfolio selection to water resource management may be cast into this framework. Severe ... Multiple objective stochastic linear programming is a relevant topic. As a matter of fact, many practical problems ranging from portfolio selection to water resource management may be cast into this framework. Severe limitations on objectivity are encountered in this field because of the simultaneous presence of randomness and conflicting goals. In such a turbulent environment, the mainstay of rational choice cannot hold and it is virtually impossible to provide a truly scientific foundation for an optimal decision. In this paper, we resort to the bounded rationality principle to introduce satisfying solution for multiobjective stochastic linear programming problems. These solutions that are based on the chance-constrained paradigm are characterized under the assumption of normality of involved random variables. Ways for singling out such solutions are also discussed and a numerical example provided for the sake of illustration. 展开更多
关键词 Satisfying Solution Chance-Constrained Multiobjective Programming Stochastic Programming
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Sufficient Optimality Conditions for Multiobjective Programming Involving (V, ρ)h,ψ-type Ⅰ Functions 认领 引用 被引量：3
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作者 ZHANG Qing-xiang JIANG Yan KANG Rui-rui 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第3期409-416,共8页
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
关键词 multiobjective programming （V,p）h,φ-type I functions Pareto efficient solu-tion sufficient optimality conditions
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Solving Bilevel Linear Multiobjective Programming Problems 认领 引用 被引量：3
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作者 Calice Olivier Pieume Patrice Marcotte +1 位作者 Laure Pauline Fotso Patrick Siarry 《American Journal of Operations Research》 2011年第4期214-219,共6页
This study addresses bilevel linear multi-objective problem issues i.e the special case of bilevel linear programming problems where each decision maker has several objective functions conflicting with each other. We ... This study addresses bilevel linear multi-objective problem issues i.e the special case of bilevel linear programming problems where each decision maker has several objective functions conflicting with each other. We introduce an artificial multi-objective linear programming problem of which resolution can permit to generate the whole feasible set of the upper level decisions. Based on this result and depending if the leader can evaluate or not his preferences for his different objective functions, two approaches for obtaining Pareto- optimal solutions are presented. 展开更多
关键词 Multiobjective Programming Bilevel Programming Feasible Solution Pareto-Optimal Solutions
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Multiobjective Stochastic Linear Programming: An Overview 认领 引用 被引量：2
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作者 A. Segun Adeyefa Monga K. Luhandjula 《American Journal of Operations Research》 2011年第4期203-213,共11页
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
关键词 Linear Programming Multiobjective Programming Stochastic Programming Expected Value Optimality/Efficiency Minimum Risk Solution/Efficiency Variance Optimality/Efficiency Optimality/Efficiency with Given Probabilities.
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Another Approach to Multiobjective Programming Problems with V-invex Functions 认领 引用 被引量：1
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作者 LIUSan-ming FENGEn-min LIXiao-shen 《Chinese Quarterly Journal of Mathematics》 北大核心 2005年第1期101-110,共10页
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
关键词 efficient solution V-invex function vector valued saddle point multiobjective programming vector valued (α,η)-Lagrange function
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The Optimality Conditions for Multiobjective Semi-infinite Programming Involving Generalized Unified (C, α, p, d)-convexity 认领 引用
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作者 ZHANG Qing-xiang ZHANG Yong-zhan 《Chinese Quarterly Journal of Mathematics》 CSCD 2013年第2期241-249,共9页
The definition of generalized unified (C, α, ρ, d)-convex function is given. The concepts of generalized unified (C, α, ρ, d)-quasiconvexity, generalized unified (C, α, ρ, d)-pseudoconvexity and generalized unif... The definition of generalized unified (C, α, ρ, d)-convex function is given. The concepts of generalized unified (C, α, ρ, d)-quasiconvexity, generalized unified (C, α, ρ, d)-pseudoconvexity and generalized unified (C, α, ρ, d)-strictly pseudoconvex functions are presented. The sufficient optimality conditions for multiobjective nonsmooth semi-infinite programming are obtained involving these generalized convexity lastly. 展开更多
关键词 generalized convexity multiobjective semi-infinite programming efficient solution optimality conditions
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Some Remarks on One Approximation Method for Nonconvex Multiobjective Programmings 认领 引用
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作者 LIANG Zhi-an 《内蒙古大学学报（自然科学版）》 CAS 北大核心 2016年第3期253-261,共9页
Some considerations have been made for one approximation method for nonconvex multiobjective programmings.Examples are given to show that the suitable constraint qualifications should be applied to ensure some corresp... Some considerations have been made for one approximation method for nonconvex multiobjective programmings.Examples are given to show that the suitable constraint qualifications should be applied to ensure some corresponding results hold in some literatures.A more general convex approximation model to a nonconvex multiobjective programming is considered and some results are obtained. 展开更多
关键词 multiobjective programming efficient solution generalized convex approximating model
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THE OPTIMALITY CONDITION AND DUALITY OF MULTIOBJECTIVE POSYNOMIAL GEOMETRIC PROGRAMMING 认领 引用
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作者 Hu Yuda Xu Ping 《Journal of Shanghai Jiaotong university(Science)》 1996年第2期1-5,共5页
This paper deals with some problems of multiobjective posynomial geometric programming. AKuhn-Tucker type optimality sufficient condition of this programming is derived. Moreover,a dual problemassociated with multiobj... This paper deals with some problems of multiobjective posynomial geometric programming. AKuhn-Tucker type optimality sufficient condition of this programming is derived. Moreover,a dual problemassociated with multiobjective posynomial geometric programming is given, and weak duality,direct dualityand inverse duality theorems are proved. 展开更多
关键词 multiobjective geometric programming K-T condition duality
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Optimality Conditions and Second-Order Duality for Nondifferentiable Multiobjective Continuous Programming Problems 认领 引用
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作者 I. Husain Vikas K. Jain 《American Journal of Operations Research》 2012年第4期536-545,共10页
Fritz John and Karush-Kuhn-Tucker type optimality conditions for a nondifferentiable multiobjective variational problem are derived. As an application of Karush-Kuhn-Tucker type optimality conditions, Mond-weir type s... Fritz John and Karush-Kuhn-Tucker type optimality conditions for a nondifferentiable multiobjective variational problem are derived. As an application of Karush-Kuhn-Tucker type optimality conditions, Mond-weir type second-order nondifferentiable multiobjective dual variational problems is constructed. Various duality results for the pair of Mond-Weir type second-order dual variational problems are proved under second-order pseudoinvexity and second-order quasi-invexity. A pair of Mond-Weir type dual variational problems with natural boundary values is formulated to derive various duality results. Finally, it is pointed out that our results can be considered as dynamic generalizations of their static counterparts existing in the literature. 展开更多
关键词 Nondifferentiable Multiobjective Programming Second-Order Invexity Second-Order Pseudoinvexity Second-Order Quasi-Invexity Second-Order Duality Nonlinear Multiobjective Programming
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