Results 31 to 40 of about 86 (54)

Corrigendum to “About contingent epiderivatives” [J. Math. Anal. Appl. 327 (2007) 745–762]

Journal of Mathematical Analysis and Applications, 2007
Rodríguez-Marín, Luis, Sama, Miguel
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Some properties of second-order contingent epiderivatives and its applications to vector equilibrium problems [PDF]

Communications in Optimization Theory, 2017
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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.
S K Zhu, Li S J, Teo K L
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Optimality conditions of the set-valued optimization problem with generalized cone convex set-valued maps characterized by contingent epiderivative

Acta Mathematicae Applicatae Sinica, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhi-Ang Zhou, Xinmin Yang, Yang Xin-Min   +2 more
exaly   +3 more sources

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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
exaly   +2 more sources

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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New second-order contingent epiderivatives and set-valued optimization problems

Acta Mathematicae Applicatae Sinica, 2016
A new concept of second-order compound contingent epiderivatives for set-valued maps is introduced, investigated and then compared to the second-order contingent epiderivative, being also employed for proposing new second-order sufficient and necessary optimality conditions for set-valued optimization problems that unify and generalize previous results
S K Zhu, Sheng-Jie Li, Li Sheng-Jie
exaly   +3 more sources

Optimality Conditions for Vector Equilibrium Problems in Terms of Contingent Epiderivatives

Numerical Functional Analysis and Optimization, 2016
ABSTRACTIn this article, we study some important properties of contingent epiderivatives concerning steady functions and a cone with a compact base along with its applications to establish necessary and sufficient optimality conditions for weakly efficient, Henig efficient, globally efficient and superefficient solutions for no constraints and ...
Tran Van Su
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Contingent epiderivatives and set-valued optimization

Mathematical Methods of Operations Research, 1997
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Johannes Jahn, Rüdiger Rauh
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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
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