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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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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 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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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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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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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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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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Higher-order Mond-Weir converse duality in multiobjective programming involving cones 认领 引用 被引量：1
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作者 YANG XinMin YANG Jin +1 位作者 YIP Tsz Leung TEO Kok Lay 《Science China Mathematics》 SCIE EI 2013年第11期2389-2392,共4页
In this work, we established a converse duality theorem for higher-order Mond-Weir type multiob- jective programming involving cones. This fills some gap in recently work of Kim et al. [Kim D S, Kang H S, Lee Y J, et ... In this work, we established a converse duality theorem for higher-order Mond-Weir type multiob- jective programming involving cones. This fills some gap in recently work of Kim et al. [Kim D S, Kang H S, Lee Y J, et al. Higher order duality in inultiobjective programming with cone constraints. Optimization, 2010, 59： 29-43]. 展开更多
关键词 multiobjective programming higher order Mond-Weir dual model converse duality theorem cones
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Connectedness of Cone-Efficient Solution Set for Cone-Quasiconvex Multiobjective Programming in Locally Convex Spaces 认领 引用 被引量：1
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作者 Xuan-weiZhou Yu-daHu 《Acta Mathematicae Applicatae Sinica》 2004年第2期309-316,共8页
This paper deals with the connectedness of the cone-efficient solution set for vector optimization inlocally convex Hausdorff topological vector spaces.The connectedness of the cone-efficient solution set is provedfor... This paper deals with the connectedness of the cone-efficient solution set for vector optimization inlocally convex Hausdorff topological vector spaces.The connectedness of the cone-efficient solution set is provedfor multiobjective programming defined by a continuous cone-quasiconvex mapping on a compact convex set ofalternatives.The generalized saddle theorem plays a key role in the proof. 展开更多
关键词 Multiobjective programming cone-efficient solution cone-quasiconvex mapping generalized saddle theorem connectedness
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Higher-order Symmetric Duality in Multiobjective Programming Problems 认领 引用 被引量：2
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作者 Ying GAO 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2016年第2期485-494,共10页
In this paper, a pair of Mond-Weir type higher-order symmetric dual programs over arbitrary cones is formulated. The appropriate duality theorems, such as weak duality theorem, strong duality theorem and converse dual... In this paper, a pair of Mond-Weir type higher-order symmetric dual programs over arbitrary cones is formulated. The appropriate duality theorems, such as weak duality theorem, strong duality theorem and converse duality theorem, are established under higher-order （strongly） cone pseudoinvexity assumptions. 展开更多
关键词 multiobjective programming problems higher-order symmetric duality higher-order cone pseu-doinvex functions
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On Nondifferentiable Higher-Order Symmetric Duality in Multiobjective Programming Involving Cones 认领 引用
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作者 Xin Min Yang Jin Yang Tsz Leung Yip 《Journal of the Operations Research Society of China》 EI 2013年第4期453-465,共13页
In this paper,we point out some deficiencies in a recent paper(Lee and Kim in J.Nonlinear Convex Anal.13:599–614,2012),and we establish strong duality and converse duality theorems for two types of nondifferentiable ... In this paper,we point out some deficiencies in a recent paper(Lee and Kim in J.Nonlinear Convex Anal.13:599–614,2012),and we establish strong duality and converse duality theorems for two types of nondifferentiable higher-order symmetric duals multiobjective programming involving cones. 展开更多
关键词 Multiobjective programming Higher-order Mond-Weir symmetric dual model Higher-order Wolfe symmetric dual model Strong duality theorems Converse duality theorems Nondifferentiability
A Smoothing Method for Solving Bilevel Multiobjective Programming Problems 认领 引用 被引量：1
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作者 Yi-Bing Lü Zhong-Ping Wan 《Journal of the Operations Research Society of China》 EI 2014年第4期511-525,共15页
In this paper,a bilevel multiobjective programming problem,where the lower level is a convex parameter multiobjective program,is concerned.Using the KKT optimality conditions of the lower level problem,this kind of pr... In this paper,a bilevel multiobjective programming problem,where the lower level is a convex parameter multiobjective program,is concerned.Using the KKT optimality conditions of the lower level problem,this kind of problem is transformed into an equivalent one-level nonsmooth multiobjective optimization problem.Then,a sequence of smooth multiobjective problems that progressively approximate the nonsmooth multiobjective problem is introduced.It is shown that the Pareto optimal solutions(stationary points)of the approximate problems converge to a Pareto optimal solution(stationary point)of the original bilevel multiobjective programming problem.Numerical results showing the viability of the smoothing approach are reported. 展开更多
关键词 Bilevel multiobjective programming Stationary point Constraint qualification Smoothing method
Second order duality for multiobjective programming with cone constraints 认领 引用 被引量：1
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作者 TANG Li Ping YAN Hong YANG Xin Min 《Science China Mathematics》 SCIE CSCD 2016年第7期1285-1306,共22页
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
关键词 multiobjective programming cone constraints second order duality
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SUFFICIENCY AND DUALITY FOR NONSMOOTH MULTIOBJECTIVE PROGRAMMING PROBLEMS INVOLVING GENERALIZED UNIVEX FUNCTIONS 认领 引用 被引量：1
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作者 LONG Xianjun 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2013年第6期1002-1018,共17页
In this paper, nonsmooth univex, nonsmooth quasiunivex, and nonsmooth pseudounivex functions are introduced. By utilizing these new concepts, sufficient optimality conditions for a weakly efficient solution of the non... In this paper, nonsmooth univex, nonsmooth quasiunivex, and nonsmooth pseudounivex functions are introduced. By utilizing these new concepts, sufficient optimality conditions for a weakly efficient solution of the nonsmooth multiobjective programming problem are established. Weak and strong duality theorems axe also derived for Mond-Weir type multiobjective dual programs. 展开更多
关键词 Duality multiobjective programming nonsmooth pseudounivexity nonsmooth quasiuni-vexity nonsmooth univexity sufficient optimality condition weakly efficient solution.
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Piecewise w∞-equitable Efficiency in Multiobjective Programming 认领 引用
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作者 D.FOROUTANNIA A.MAHMODINEJAD 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2017年第3期825-836,共12页
In equitable multiobjective optimization all the objectives are uniformly optimized, but in some cases the decision maker believes that some of them should be uniformly optimized according to the importance of objecti... In equitable multiobjective optimization all the objectives are uniformly optimized, but in some cases the decision maker believes that some of them should be uniformly optimized according to the importance of objectives. To solve this problem in this paper, the original problem is decomposed into a collection of smaller subproblems, according to the decision maker, and the subproblems are solved by the concept of wr- equitable efficiency, where w ∈ R＋ m is a weight vector. First some theoretical and practical aspects of Pwr- equitably efficient solutions are discussed and by using the concept of Pwr-equitable efficiency one model is presented to coordinate weakly wr-equitable efficient solutions of subproblems. Then the concept of Pw ∞- equitable is introduced to generate subsets of equitably efficient solutions, which aims to offer a limited number of representative solutions to the decision maker. 展开更多
关键词 pareto nondominated equitability decomposition coordination multiobjective programming
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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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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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Nondifferentiable Multiobjective Programming under Generalized d-ρ-(η,θ)-Type I Univexity 认领 引用
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作者 Chun Feng WANG San Yang LIU 《Journal of Mathematical Research and Exposition》 CSCD 2011年第4期655-664,共10页
In this puper, on the basis of notions of d-p-（η, θ）-invex function, type I function and univex function, we present new classes of generalized d-p-（η, θ）-type I univex functions. By using these new concepts, ... In this puper, on the basis of notions of d-p-（η, θ）-invex function, type I function and univex function, we present new classes of generalized d-p-（η, θ）-type I univex functions. By using these new concepts, we obtain several sufficient optimality conditions for a feasible solution to be an efficient solution, and derive some Mond-Weir type duality results. 展开更多
关键词 multiobjective programming generalized d-p-（η, θ）-type I univexity duality optimality.
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DUALITY FOR A CLASS OF NONS MOOTH MULTIOBJECTIVE PROGRAMMING PROBLEMS 认领 引用
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作者 PENGJianwen YANGXinmin 《Journal of Systems Science & Complexity》 2005年第1期74-85,共12页
In this paper, two new dual models of nonsmooth multiobjective programmingare constructed and two duality results are derived.
关键词 locally lipschitz function multiobjective programming generalizedconvexity duality theorems
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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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