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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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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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Chance-Constrained Approaches for Multiobjective Stochastic Linear Programming Problems 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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Solving Bilevel Linear Multiobjective Programming Problems 被引量:2
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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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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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THE OPTIMALITY CONDITION AND DUALITY OF MULTIOBJECTIVE POSYNOMIAL GEOMETRIC PROGRAMMING
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作者 Hu Yuda Xu Ping(Dept. of Applied Mathematics) 《Journal of Shanghai Jiaotong university(Science)》 EI 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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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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An Interactive Fuzzy Satisficing Method for Multiobjective Stochastic Integer Programming with Simple Recourse
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作者 Masatoshi Sakawa Takeshi Matsui 《Applied Mathematics》 2012年第10期1245-1251,共7页
This paper considers multiobjective integer programming problems involving random variables in constraints. Using the concept of simple recourse, the formulated multiobjective stochastic simple recourse problems are t... This paper considers multiobjective integer programming problems involving random variables in constraints. Using the concept of simple recourse, the formulated multiobjective stochastic simple recourse problems are transformed into deterministic ones. For solving transformed deterministic problems efficiently, we also introduce genetic algorithms with double strings for nonlinear integer programming problems. Taking into account vagueness of judgments of the decision maker, an interactive fuzzy satisficing method is presented. In the proposed interactive method, after determineing the fuzzy goals of the decision maker, a satisficing solution for the decision maker is derived efficiently by updating the reference membership levels of the decision maker. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method. 展开更多
关键词 multiobjective programming Stochastic programming FUZZY programming INTERACTIVE Methods SIMPLE RECOURSE Model
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MAJOR-EFFICIENT SOLUTIONS AND WEAKLY MAJOR-EFFICIENT SOLUTIONS OF MULTIOBJECTIVE PROGRAMMING
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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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Efficiency and Duality in Nondifferentiable Multiobjective Programming Involving Directional Derivative
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作者 Izhar Ahmad 《Applied Mathematics》 2011年第4期452-460,共9页
In this paper, we introduce a new class of generalized dI-univexity in which each component of the objective and constraint functions is directionally differentiable in its own direction di for a nondifferentiable mul... In this paper, we introduce a new class of generalized dI-univexity in which each component of the objective and constraint functions is directionally differentiable in its own direction di for a nondifferentiable multiobjective programming problem. Based upon these generalized functions, sufficient optimality conditions are established for a feasible point to be efficient and properly efficient under the generalised dI-univexity requirements. Moreover, weak, strong and strict converse duality theorems are also derived for Mond-Weir type dual programs. 展开更多
关键词 multiobjective programming NONDIFFERENTIABLE programming Generalized dI-Univexity SUFFICIENCY 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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A Weaker Constraint Qualification of Globally Convergent Homotopy Method for a Multiobjective Programming Problem
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作者 Guangming Yao Wen Song 《Applied Mathematics》 2013年第2期343-347,共5页
In this paper, we prove that the combined homotopy interior point method for a multiobjective programming problem introduced in Ref. [1] remains valid under a weaker constrained qualification—the Mangasarian-Fromovit... In this paper, we prove that the combined homotopy interior point method for a multiobjective programming problem introduced in Ref. [1] remains valid under a weaker constrained qualification—the Mangasarian-Fromovitz constrained qualification, instead of linear independence constraint qualification. The algorithm generated by this method associated to the Karush-Kuhn-Tucker points of the multiobjective programming problem is proved to be globally convergent. 展开更多
关键词 multiobjective programming PROBLEM HOMOTOPY Method KKT CONDITION Efficient Solution MFCQ
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Sufficiency and Wolfe Type Duality for Nonsmooth Multiobjective Programming Problems
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作者 Gang An Xiaoyan Gao 《Advances in Pure Mathematics》 2018年第8期755-763,共9页
In this paper, a class of nonsmooth multiobjective programming problems is considered. We introduce the new concept of invex of order??type II for nondifferentiable locally Lipschitz functions using the tools of Clark... In this paper, a class of nonsmooth multiobjective programming problems is considered. We introduce the new concept of invex of order??type II for nondifferentiable locally Lipschitz functions using the tools of Clarke subdifferential. The new functions are used to derive the sufficient optimality condition for a class of nonsmooth multiobjective programming problems. Utilizing the sufficient optimality conditions, weak and strong duality theorems are established for Wolfe type duality model. 展开更多
关键词 multiobjective programming OPTIMALITY Condition Locally LIPSCHITZ Function Wolfe TYPE Dual Problem
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Nondifferentiable Multiobjective Programming with Equality and Inequality Constraints
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作者 Iqbal Husain Vikas K. Jain 《Open Journal of Modelling and Simulation》 2013年第2期7-13,共7页
In this paper, we derive optimality conditions for a nondifferentiable multiobjective programming problem containing a certain square root of a quadratic form in each component of the objective function in the presenc... In this paper, we derive optimality conditions for a nondifferentiable multiobjective programming problem containing a certain square root of a quadratic form in each component of the objective function in the presence of equality and inequality constraints. As an application of Karush-Kuhn-Tucker type optimality conditions, a Mond-Weir type dual to this problem is formulated and various duality results are established under generalized invexity assumptions. Finally, a special case is deduced from our result. 展开更多
关键词 NONDIFFERENTIABLE multiobjective programming Problem Efficient Solution Generalized INVEXITY DUALITY NONDIFFERENTIABLE multiobjective programming Problems with EQUALITY and Inequality
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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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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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A New Interactive Method to Solve Multiobjective Linear Programming Problems
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作者 Mahmood REZAEI SADRABADI Seyed Jafar SADJADI 《Journal of Software Engineering and Applications》 2009年第4期237-247,共11页
Multiobjective Programming (MOP) has become famous among many researchers due to more practical and realistic applications. A lot of methods have been proposed especially during the past four decades. In this paper, w... Multiobjective Programming (MOP) has become famous among many researchers due to more practical and realistic applications. A lot of methods have been proposed especially during the past four decades. In this paper, we develop a new algorithm based on a new approach to solve MOP by starting from a utopian point, which is usually infeasible, and moving towards the feasible region via stepwise movements and a simple continuous interaction with decision maker. We consider the case where all objective functions and constraints are linear. The implementation of the pro-posed algorithm is demonstrated by two numerical examples. 展开更多
关键词 multiobjective Linear programming multiobjective DECISION MAKING INTERACTIVE Methods
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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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