Results 61 to 70 of about 140 (77)

Set-Valued Approach to Hamilton-Jacobi-Bellman Equations [PDF]

, 1992
Frankowska, H., Plaskacz, S., Rzezuchowski, T.   +2 more
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-contingent epiderivatives in reflexive spaces

Nonlinear Analysis: Theory, Methods & Applications, 2008
Abstract In this paper we introduce a notion of the τ w -contingent epiderivative of a set-valued map by considering the weak topology in the image space. We establish a chain rule formula for families of τ w -contingent and contingent epiderivatives.
Luis Rodríguez-Marín, Miguel Sama
openaire   +1 more source

Some Calculus Rules for Contingent Epiderivatives

Optimization, 2003
This article presents some calculus rules for contingent epiderivatives of set-valued maps. Among other results the main emphasis is focused on a formula for scalar multiplication, sum formulae and chain rules. The calculus of contingent cones and some inversion theorems are used as a tool. Some applications are also given.
Johannes Jahn, Akhtar A. Khan
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Contingent epiderivatives and set-valued optimization

Mathematical Methods of Operations Research, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jahn, Johannes, Rauh, Rüdiger
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GENERALIZED CONTINGENT EPIDERIVATIVES IN SET-VALUED OPTIMIZATION: OPTIMALITY CONDITIONS

Numerical Functional Analysis and Optimization, 2002
ABSTRACT Necessary and sufficient optimality conditions are given for various optimality notions in set-valued optimization. These optimality conditions are given by employing the generalized contingent epiderivative and the weak contingent epiderivative of the objective set-valued map and the set-valued map defining the constraints. The known Lagrange
Johannes Jahn, Akhtar A. Khan
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Second-Order Modified Contingent Epiderivatives in Set-Valued Optimization

Numerical Functional Analysis and Optimization, 2013
In this article, we introduce a second-order modified contingent cone and a second-order modified contingent epiderivative. We discuss some properties of the second-order cone and the epiderivative, respectively. Moreover, a Fritz John type necessary optimality condition is obtained for the set-valued optimization problems with constraints by using the
Ben Liu, Kairong Wang
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Second-order weakly composed adjacent-generalized contingent epiderivatives and applications to composite set-valued optimization problems

Japan Journal of Industrial and Applied Mathematics, 2021
New second-order weakly composed adjacent-generalized contingent epiderivatives for set-valued maps are introduced and investigated, in particular sum and chain rules for them being provided. These epiderivatives are afterwards employed in establishing necessary and sufficient optimality conditions for characterizing Benson proper efficient solutions ...
Tang, Tian, Wang, Qilin, Zhang, Xiaoyan, Zhai, Yuwen   +3 more
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New Generalized Second-Order Contingent Epiderivatives and Set-Valued Optimization Problems

Journal of Optimization Theory and Applications, 2011
The authors introduce a new generalized second-order contingent epiderivative for set-valued maps. Using it, one obtains a significant unified sufficient and necessary optimality condition for set-valued optimization problems.
Li, S, Zhu, S, Teo, Kok Lay
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Optimality conditions in terms of contingent epiderivatives for strict local Pareto minima in vector optimization problems with constraints

Positivity, 2021
The paper addresses primal and dual necessary and sufficient optimality conditions for strict local Pareto minima (also known as isolated local Pareto mimima) of a nonsmooth constrained vector optimization problem. Specifically, the feasible set of the problem is defined by set, cone and equality constraints and the objective and constraint functions ...
Tran Van Su, Dinh Dieu Hang
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Generalized second-order contingent epiderivatives in parametric vector optimization problems

Journal of Global Optimization, 2013
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Sun, Xiang-Kai, Li, Sheng-Jie
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