Search Results - Directional coderivative

Calculus of directional coderivatives and normal cones in Asplund spaces by Long, Pujun, Wang, Bingwu, Yang, Xinmin

“…We study the directional Mordukhovich normal cones to nonsmooth sets, coderivatives of set-valued mappings in Asplund spaces and establish extensive calculus results on these constructions…”
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Directionally generalized differentiation for multifunctions and applications to set-valued programming problems by Thinh, Vo Duc, Chuong, Thai Doan

“…The aim of this work is twofold. First, we establish sum rules for the directionally coderivatives of multifunctions and intersection rules for the directionally limiting normal cones…”
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Calculus of directional subdifferentials and coderivatives in Banach spaces by Long, Pujun, Wang, Bingwu, Yang, Xinmin

“…In this work we study the directional versions of Mordukhovich normal cones to nonsmooth sets, coderivatives of set-valued mappings, and subdifferentials of extended-real-valued functions…”
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On the Aubin property of solution maps to parameterized variational systems with implicit constraints by Gfrerer, Helmut, Outrata, Jiří V.

“… of implicitly defined multifunctions which employs the recently introduced notion of the directional limiting coderivative…”
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On the Aubin property of a class of parameterized variational systems by Gfrerer, H., Outrata, J. V.

“… The new condition requires computation of directional limiting coderivatives of the normal-cone mapping for the so-called critical directions…”
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On the directional asymptotic approach in optimization theory by Benko, Matúš, Mehlitz, Patrick

“… (corresponding to stationarity of order 1), satisfies stationarity conditions in terms of a coderivative construction of order $$\gamma $$ γ…”
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Some Minimax Type Results Of Clarke's Generalized Directional Derivative And Point-Coderivative Of Multifunctions by Isac, G., Li, J. L.

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Projectional Coderivatives and Calculus Rules by Yao, Wenfang, Meng, Kaiwen, Li, Minghua, Yang, Xiaoqi

“…This paper is devoted to the study of a newly introduced tool, projectional coderivatives, and the corresponding calculus rules in finite dimensional spaces…”
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Coderivative and Graphical Derivative of the Metric Projection onto Closed Balls in Hilbert Spaces by Hien, Le Van

“…In this paper, we first derive an exact formula for computing the regular coderivative of the metric projection operator onto closed balls r B centered at the origin in Hilbert spaces…”
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A Hausdorff-type distance, a directional derivative of a set-valued map and applications in set optimization by Ha, Truong Xuan Duc

“… We introduce a Hausdorff-type distance relative to an ordering cone between two sets in a Banach space and use it to define a directional derivative for F…”
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Directional Metric Pseudo Subregularity of Set-valued Mappings: a General Model by Van Ngai, Huynh, Tron, Nguyen Huu, Van Vu, Nguyen, Théra, Michel

“…)regularity models studied recently in the literature. Some slope and abstract coderivative characterizations are established…”
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Directional Hölder Metric Regularity by Van Ngai, Huynh, Tron, Nguyen Huu, Théra, Michel

“…This paper sheds new light on regularity of multifunctions through various characterizations of directional…”
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On the directional asymptotic approach in optimization theory: The directional asymptotic approach by Benko, Matúš, Mehlitz, Patrick

“… (corresponding to stationarity of order 1), satisfies stationarity conditions in terms of a coderivative construction of order γ…”
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Metric Regularity Relative to a Cone by Van Ngai, Huynh, Tron, Nguyen Huu, Théra, Michel

“… For example, we establish a slope and some coderivative characterizations of this concept, as well as some stability results with respect to a Lipschitz perturbation…”
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Calculus for Directional Limiting Normal Cones and Subdifferentials by Benko, Matúš, Gfrerer, Helmut, Outrata, Jiří V.

“…The paper is devoted to the development of a comprehensive calculus for directional limiting normal cones, subdifferentials and coderivatives in finite dimensions…”
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Lipschitz-like property relative to a set and the generalized Mordukhovich criterion by Meng, K. W., Li, M. H., Yao, W. F., Yang, X. Q.

“… We will obtain a complete characterization for a set-valued mapping to have the Lipschitz-property relative to a closed and convex set by virtue of the projection of the coderivative onto a tangent cone…”
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Directionally generalized differentiation and applications to set-valued optimization, multiobjective optimal control problems by Toan, N. T., Thuy, L. Q.

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Estimates of Generalized Hessians for Optimal Value Functions in Mathematical Programming by Zemkoho, Alain B.

“… However, the differentiability aspect of works in the current literature has mostly been limited to first order analysis, with focus on estimates of its directional derivatives and subdifferentials…”
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On Lipschitzian properties of implicit multifunctions by Gfrerer, Helmut, Outrata, Jiří V

“… As the basic tool one employs the directional limiting coderivative which, together with the graphical derivative, enable us a fine analysis of the local behavior of the investigated multifunction…”
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DIRECTIONAL COMPACTNESS, SCALARIZATION AND NONSMOOTH SEMI-FREDHOLM MAPPINGS by IOFFE, A.D.

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