Search Results - coderivatives of set-valued maps*

Constraint Qualifications and Necessary Optimality Conditions for Optimization Problems with Variational Inequality Constraints by Ye, J. J.

“… Fritz John type and Kuhn--Tucker type necessary optimality conditions involving Mordukhovich coderivatives are derived…”
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The Ekeland variational principle for set-valued maps involving coderivatives by Ha, Truong Xuan Duc

“…In this paper we use the Fréchet, Clarke, and Mordukhovich coderivatives to obtain variants of the Ekeland variational principle for a set-valued map F and establish optimality conditions for set-valued optimization problems…”
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Coderivatives and Aubin property of efficient point and efficient solution set-valued maps in parametric vector optimization by Xue, Xiaowei

“…The aim of this paper is computing the coderivatives of efficient point and efficient solution set-valued maps in a parametric vector optimization problem…”
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Coderivatives of gap function for Minty vector variational inequality by Xue, Xiaowei, Zhang, Yu

“… First, we discuss the regular coderivative, the normal coderivative, and the mixed coderivative of a class of set-valued maps…”
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Derivatives and Epiderivatives of Set-Valued Maps by Khan, Akhtar A, Tammer, Christiane, Zălinescu, Constantin

“…In set-valued optimization, derivatives, epiderivatives, and coderivatives of set-valued maps play the most fundamental role…”
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Set-Valued Return Function and Generalized Solutions for Multiobjective Optimal Control Problems (MOC) by Guigue, A.

“…$ and provide a unique characterization for $V$ in terms of contingent derivative and coderivative for set-valued maps, which extends two previously introduced notions of generalized solution to the Hamilton--Jacobi equation for single objective…”
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Geometric approach to convex subdifferential calculus by Mordukhovich, Boris S., Nam, Nguyen Mau

“… optimal value/marginal functions, normals to inverse images of sets under set-valued mappings, calculus rules for coderivatives of single-valued and set-valued mappings, and calculating coderivatives…”
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Sufficient conditions for reachability and controllability of discrete systems with phase constraints by Sach, P.H.

“… The main tools one uses are different notions of coderivatives of set-valued maps and normal cones of sets…”
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Coderivatives in parametric optimization by Levy, Adam B., Mordukhovich, Boris S.

“… Coderivatives of set-valued mappings are our basic tool to analyze the parametric sensitivity of either stationary points or stationary point-multiplier pairs associated with parameterized optimization problems…”
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Sensitivity Analysis in Parametric Convex Vector Optimization by An, Duong Thi Viet, Tung, Le Thanh

“… Namely, the perturbation, weak perturbation, and proper perturbation maps are defined as set-valued maps…”
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Sensitivity Analysis for Two-Level Value Functions with Applications to Bilevel Programming by Dempe, S., Mordukhovich, B. S., Zemkoho, A. B.

“… bilevel program appropriate coderivative constructions for the set…”
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Strict Efficiency in Set Optimization Studied with the Set Approach by Ha, Truong Xuan Duc

“… In particular, we establish some conditions expressed in terms of a high-order directional derivative of set-valued maps and the (convex or limiting…”
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Geometric Approach to Subdifferential Calculus by Mordukhovich, Boris, Nguyen Mau Nam

“… marginal/value functions, normal of inverse images of sets under set-valued mappings, calculus rules for coderivatives of single-valued and set-valued mappings, and calculating coderivatives of solution…”
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Codifferential Calculus by Li, Shengjie, Penot, Jean-Paul, Xue, Xiaowei

“… Similar rules are displayed for sums. A crucial role is played by an intermediate set-valued map called the resolvent…”
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Set-Valued Return Function and Generalized Solutions for Multiobjective Optimal Control Problems (MOC) by Guigue, A

“…, which defines generalized Pareto optimality. For this problem, we introduce the set-valued return function V and provide a unique characterization for V in terms of contingent derivative and coderivative for set-valued maps, which extends two…”
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Generalized Differential Calculus and Applications to Optimization by Rector, Robert Blake Hayden

“… These advances specifically pertain to methods for calculating subdifferentials and to expanding our understanding of a certain notion of derivative of set-valued maps, called the coderivative, in infinite dimensions…”
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Sensitivity Analysis in Parametric Convex Vector Optimization by Duong Thi Viet An, Le Thanh Tung

“… Namely, the perturbation, weak perturbation, and proper perturbation maps are defined as set-valued maps…”
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Some Variants of the Ekeland Variational Principle for a Set-Valued Map by Ha, T. X. D.

“…This paper deals with the Ekeland variational principle (EVP) for a set-valued map F with values in a vector space E…”
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Sensitivity analysis of gap functions for vector variational inequality via coderivatives by Li, S.J., Xue, X.W.

“…The aim of this article is to investigate codifferential properties of a class of set-valued maps and gap function involving vector variational inequality…”
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Generalized differentiation with positively homogeneous maps: Applications in set-valued analysis and metric regularity by Pang, C H Jeffrey

“… continuity in set-valued maps. We present calculus rules, sharpen the relationship between the Aubin property and coderivatives, and study how metric regularity and open covering can be refined to have a directional property…”
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