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Higher-order generalized tangent epiderivatives and applications to set-valued optimization
In the paper, we introduce two new concepts on differentiability for set-valued maps, named by the higher-order generalized tangent epiderivative and...
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A note on “Higher-order generalized Studniarski epiderivative and its applications in set-valued optimization” [Positivity 22:1371–1385 (2018)]
In this note, we establish a property of the higher-order generalized Studniarski epiderivative. By virtue of the property, we demonstrate that...
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Higher-order tangent epiderivatives and applications to duality in set-valued optimization
In the paper, we introduce higher-order tangent epiderivatives for set-valued maps. Then, we study some basic properties of these concepts. Finally,...
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Higher-order tangent derivative and its applications to sensitivity analysis
In the paper, we study the higher-order tangent derivative for set-valued maps. More precisely, we first develop its calculus rules. Then, via this...
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Second-order weakly composed adjacent-generalized contingent epiderivatives and applications to composite set-valued optimization problems
In the paper, we introduce the second-order weakly composed adjacent-generalized contingent epiderivative for set-valued maps. Then we gain a few...
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On Necessary Optimality Conditions with Higher-Order Complementarity Slackness for Set-Valued Optimization Problems
We aim to establish Karush-Kuhn-Tucker multiplier rules involving higher-order complementarity slackness under Hölder metric subregularity. These...
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New higher-order weak lower inner epiderivatives and application to Karush–Kuhn–Tucker necessary optimality conditions in set-valued optimization
The purpose of the paper is to establish higher-order Karush–Kuhn–Tucker higher-order necessary optimality conditions for set-valued optimization...
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New Higher-Order Strong Karush–Kuhn–Tucker Conditions for Proper Solutions in Nonsmooth Optimization
This paper considers higher-order necessary conditions for Henig-proper, positively proper and Benson-proper solutions. Under suitable constraint...
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Robust duality for robust efficient solutions in uncertain vector optimization problems
In this paper, we introduce second-order subdifferentials of vector-valued maps and single-valued maps, respectively, and discuss some properties of...
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Quasi-contingent derivatives and studies of higher-orders in nonsmooth optimization
We consider higher-order conditions and sensitivity analysis for solutions to equilibrium problems. The conditions for solutions are in terms of...
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Karush–Kuhn–Tucker Multiplier Rules for Efficient Solutions of Set-Valued Equilibrium Problem with Constraints
In this paper, a type of contingent derivative of a set-valued map is proposed and applied to investigate some necessary optimality conditions for...
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New Second-Order Tangent Epiderivatives and Applications to Set-Valued Optimization
A new second-order tangent set is introduced, with which a new second-order tangent epiderivative is also introduced for a set-valued map. Applying a...
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Mathematical Tools of Dynamic Systems in Hilbert Spaces
In this chapter, dynamic systemsDynamic system and solutionSpace- Hilbert concepts are reviewed in the infinite-dimensional setting. After brief...
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Second-Order Karush–Kuhn–Tucker Optimality Conditions for Set-Valued Optimization Subject to Mixed Constraints
In this paper, we propose the concept of second-order composed adjacent contingent derivatives for set-valued maps and hence discuss the included...
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Second-order composed contingent derivatives of perturbation maps in set-valued optimization
In the paper, we study calculus rules of second-order composed contingent derivatives. More precisely, chain rule and sum rule are established and...
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On Higher-Order Mixed Duality in Set-Valued Optimization
In the paper, we first develop sum and chain rules of higher-order radial derivatives. By virtue of these derivatives, we establish duality theorems...
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Mathematical Appendixes
We gather and summarize in this heteroclite chapter some definitions and results used in this book for easing its reading: Sect. 8.1, p. 211,...
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Second-Order Conditions for Open-Cone Minimizers and Firm Minimizers in Set-Valued Optimization Subject to Mixed Constraints
We consider second-order optimality conditions for set-valued optimization problems subject to mixed constraints. Such optimization models are useful...
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Second-order composed contingent epiderivatives and set-valued vector equilibrium problems
In this paper, we introduce the concept of a second-order composed contingent epiderivative for set-valued maps and discuss some of its properties....
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Introduction
Set-valued optimization is a vibrant and expanding branch of applied mathematics that deals with optimization problems where the objective map and/or...