Duality in geometric vector optimization

Elster, Rosalind; Gerth, Christiane; Göpfert, A.

doi:10.1080/02331938908843464

Cited by 6 publications

(2 citation statements)

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“…In this respect we refer the reader to [5,9,10,12,27,28,30,31] and references therein. The general theory of multiobjective optimization can be found in the monographs [6,11,12,14,23] and the bibliographies there.…”

Section: Introductionmentioning

confidence: 99%

Pareto optimality and Walrasian equilibria

Naniewicz

2008

Journal of Mathematical Analysis and Applications

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The paper concerns the study of a class of convex, constrained multiobjective optimization problems from the viewpoint of the existence issues. The main feature of the presented approach is that the classical qualification condition requiring the existence of interior points in the effective domains of functions under consideration does not hold. A variant of duality theory for multiobjective optimization problems based on the Fenchel theorem is formulated. Next, by using very recent results on the Walrasian general equilibrium model of economy obtained in Naniewicz [Z. Naniewicz, Pseudo-monotonicity and economic equilibrium problem in reflexive Banach space, Math. Oper. Res. 32 (2007) 436-466] the conditions ensuring the existence of Pareto optimal solutions for the class of multiobjective optimization problems are established. The concept of the proper efficiency is used as the solution notion. Finally, a new version of the second fundamental theorem of welfare economics is presented.

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Section: Introductionmentioning

confidence: 99%

Pareto optimality and Walrasian equilibria

Naniewicz

2008

Journal of Mathematical Analysis and Applications

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“…For (27) we need (18). Namely, taking into account that α n j x n α j x and π n j π j weakly in X and X , respectively, by (26) we get…”

Section: Propositionmentioning

confidence: 99%

On Economic Equilibrium Type Problems with Applications

Naniewicz

2010

Set-Valued Anal

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The existence solution for a class of economic equilibrium type problems in reflexive Banach space is considered. New results concerning the variational inequality approach to Arrow-Debreu model of economic equilibrium introduced in Naniewicz (Math Oper Res 32:436-466, 2007) are found and applied to ensure the existence of Pareto optimal solutions for a class of multiobjective optimization problems with so-called budget-like constraints. To achieve this goal, the theory of pseudo-monotone multivalued mappings combined with some fixed point technique for multivalued mappings with nonconvex values is used.

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Nonlinear Multiobjective Programming

Tanino

Kuk

2003

International Series in Operations Research &Amp; Management Science

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Duality in geometric vector optimization

Cited by 6 publications

References 6 publications

Pareto optimality and Walrasian equilibria

Pareto optimality and Walrasian equilibria

On Economic Equilibrium Type Problems with Applications

Nonlinear Multiobjective Programming

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