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MAJOR-EFFICIENT SOLUTIONS AND WEAKLY MAJOR-EFFICIENT SOLUTIONS OF MULTIOBJECTIVE PROGRAMMING 被引量:12
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作者 HU YUDA(Dept.of Appl.Math.,Shanghai Jiao Tony Univ.,Shanghai 200030) 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 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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Sufficient Optimality Conditions for Multiobjective Programming Involving (V, ρ)h,ψ-type Ⅰ Functions 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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Sufficiency and Duality for Nondif ferentiable Multiobjective Fractional Programming Problems with (Φ,ρ,α)-V-Invexity 被引量:2
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作者 闫春雷 杨舒先 《Journal of Donghua University(English Edition)》 EI 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 ρ α)-V-invexity SUFFICIENCY DUALITY
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Connectedness of Cone-efficient Solution Set for Cone-quasiconvex Multiobjective Programming in Hausdorff Topological Vector Spaces 被引量:1
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作者 ZHOU Xuan-wei 《Chinese Quarterly Journal of Mathematics》 CSCD 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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Another Approach to Multiobjective Programming Problems with V-invex Functions 被引量:1
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作者 LIUSan-ming FENGEn-min LIXiao-shen 《Chinese Quarterly Journal of Mathematics》 CSCD 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 η)-Lagrange function
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Optimality conditions and duality for a class of nondifferentiable multiobjective generalized fractional programming problems 被引量:1
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作者 GAO Ying RONG Wei-dong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 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 ... 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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Optimality Conditions and Duality for Nonsmooth Multiobjective Programms with Generalized Essential Convexity 被引量:1
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作者 王彩玲 刘庆怀 李忠范 《Northeastern Mathematical Journal》 CSCD 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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Multiobjective Decision Making: the Combined Approach
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作者 Feng JunwenSoft-Science Research Institute, East China Institute of Technology, Nanjing 210014, China 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 1992年第2期57-65,共9页
In this paper, a new approach for generating all or partly efficient solutions called the Combined Approach is developed. The property of efficient solutions generated by the combined approach and its relationships wi... In this paper, a new approach for generating all or partly efficient solutions called the Combined Approach is developed. The property of efficient solutions generated by the combined approach and its relationships with other four approaches: weighting approach, sequential approach, ε-constraint approach and hybrid approach, are discussed. Based on this combined approach, a decision-making support method called the Combined Decision-Making Method (CDMM) for multiobjective problems is developed, which is an interactive process with the decision maker. Only the aspiration levels, which reflect the decision maker's satisfying degrees for corresponding objectives, are needed to be supplied by the decision maker step by step as he will. This interactive way for objectives can easily be accepted. Finally, the application of the proposed decision making method in the resource allocation problem is discussed, and an example for the production decision analysis of the solar energy cells given. 展开更多
关键词 multiobjective decision-making EFFICIENCY Decision analysis Vector optimization multiobjective programming.
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DUALITY FOR MULTIOBJECTIVE FRACTIONAL PROGRAMMING INVOLVING n-SET FUNCTIONS
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作者 陈世国 刘家学 《Acta Mathematica Scientia》 SCIE CSCD 1998年第S1期36-42,共7页
In this paper, two duality results are established under generalized ρ-convexity conditions for a class of multiobjective fractional programmign involvign differentiable n-sten functions.
关键词 n-set functions ρ-convexity strictly quasiconvex multiobjective fractional programming DUALITY
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The Optimality Conditions for Multiobjective Semi-infinite Programming Involving Generalized Unified (C, α, p, d)-convexity
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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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Nondifferentiable Multiobjective Programming under Generalized d_I-G-Type I Invexity
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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 invexity sufficient optimality conditions dualityCLC number:O221.6Document code:AArticle ID:1672-5220(2013)04-0293-05
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Duality for Dini-Invex Nonsmooth Multiobjective Programming
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作者 李忠范 刘庆怀 杨荣 《Northeastern Mathematical Journal》 CSCD 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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THE SUFFICIENT EFFICIENCY CONDITIONS IN SEMIINFINITE MULTIOBJECTIVE FRACTIONAL PROGRAMMING UNDER HIGHER ORDER EXPONENTIAL TYPE HYBRID TYPE INVEXITIES
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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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Necessary and Sufficient Conditions in Smooth Programming with Generalized Convexity 被引量:1
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作者 孙清滢 叶留青 《Chinese Quarterly Journal of Mathematics》 CSCD 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 functions
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OPTIMALITY CONDITIONS AND DUALITY RESULTS FOR NONSMOOTH VECTOR OPTIMIZATION PROBLEMS WITH THE MULTIPLE INTERVAL-VALUED OBJECTIVE FUNCTION 被引量:4
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作者 Tadeusz ANTCZAK 《Acta Mathematica Scientia》 SCIE CSCD 2017年第4期1133-1150,共18页
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
关键词 nonsmooth multiobjective programming problem with the multiple interval- objective function Fritz John necessary optimality conditions Karush-Kuhn- Tucker necessary optimality conditions (weakly) LU-efficient solution Mond- Weir duality
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Multi-objective Programming and Social Welfare Analysis of Rural–urban Land Conversion Decision-making
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作者 Song Min Zhang Anlu 《Chinese Journal of Population,Resources and Environment》 北大核心 2008年第4期65-71,共7页
Rural-urban land conversion is an inevitable phenomenon in urbanization arid industrialization. And the decision-making issue about this conversion is multi-objective because the social decision maker (the whole of c... Rural-urban land conversion is an inevitable phenomenon in urbanization arid industrialization. And the decision-making issue about this conversion is multi-objective because the social decision maker (the whole of central government and local authority) has to integrate the requirements of different interest groups (rural collective economic organizations, peasants, urban land users and the ones affected indirectly) and harmonize the sub-objects (economic, social and ecological outcomes) of this land allocation process. This paper established a multi-objective programming model for rural-urban land conversion decision-making and made some social welfare analysis correspondingly. Result shows that the general object of rural-urban land conversion decision-making is to reach the optimal level of social welfare in a certain state of resources allocation, while the preference of social decision makers and the value judgment of interest groups are two crucial factors which determine the realization of the rural-urban land conversion decision-making objects. 展开更多
关键词 ntral-urban land conversion DECISION-MAKING multiobjective programming social welfare
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Higher-order Symmetric Duality in Multiobjective Programming Problems 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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Connectedness of Cone-Efficient Solution Set for Cone-Quasiconvex Multiobjective Programming in Locally Convex Spaces 被引量:1
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作者 Xuan-weiZhou Yu-daHu 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 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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SUFFICIENCY AND DUALITY FOR NONSMOOTH MULTIOBJECTIVE PROGRAMMING PROBLEMS INVOLVING GENERALIZED UNIVEX FUNCTIONS 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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Higher-order Mond-Weir converse duality in multiobjective programming involving cones 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 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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