Search Results - Clarke coderivative

The Clarke Coderivative of the Frontier Map in a Multi-objective Optimal Control Problem by Toan, N. T., Thuy, L. Q.

“… By establishing an abstract result on the Clarke coderivative of the frontier map of a multi-objective parametric mathematical programming problem, we derive a formula for computing the Clarke…”
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Clarke coderivatives of efficient point multifunctions in parametric vector optimization by Chuong, Thai Doan

“…The paper is devoted to the study of the Clarke/circatangent coderivatives of the efficient point multifunction of parametric vector optimization problems in Banach spaces…”
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Stability of Implicit Multifunctions in Banach Spaces by Huy, N. Q., Kim, D. S., Ninh, K. V.

“… The basic tools of our analysis involve the Clarke subdifferential, the Clarke coderivative of set-valued mappings, and the Ekeland variational principle…”
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On Several Types of Basic Constraint Qualifications via Coderivatives for Generalized Equations by Wei, Zhou, Yao, Jen-Chih

“…In this paper, we study several types of basic constraint qualifications in terms of Clarke…”
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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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Metric regularity of a positive order for generalized equations by Chuong, Thai Doan

“… The provided conditions are expressed in terms of the Fréchet coderivative/or the Mordukhovich coderivative/or the Clarke one of the corresponding multifunction formulated the generalized equation…”
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The Lagrange multiplier rule for super efficiency in vector optimization by Huang, H.

“… In terms of the coderivatives and Clarke's normal cones, we establish Lagrange multiplier rules for super efficiency as necessary or sufficient optimality conditions…”
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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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The Ekeland variational principle for Henig proper minimizers and super minimizers by Ha, Truong Xuan Duc

“… two versions of the Ekeland variational principle for these points involving coderivatives in the sense of Ioffe, Clarke and Mordukhovich…”
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Implicit Multifunction Theorems in Banach Spaces by Yang, Ming-ge, Xu, Yi-fan

“…This paper is mainly devoted to the study of implicit multifunction theorems in terms of Clarke coderivative in general Banach spaces…”
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Variants of the Ekeland Variational Principle for a set-valued map involving the Clarke Normal Cone by Ha, Truong Xuan Duc

“…In this paper we present two set-valued variants of the Ekeland variational principle involving the Clarke normal cone and establish sufficient conditions for a set-valued map to have a weak minimizer…”
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Characterization of Convex and Generalized Convex Vector Fields on Riemannian Manifolds by Ghahraei, Elham

“… The inclusive relations between Clarke generalized Jacobian and Mordukhovich coderivative and this subdifferential are proved…”
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A Unified Approach to Convex and Convexified Generalized Differentiation of Nonsmooth Functions and Set-Valued Mappings by Nam, Nguyen Mau, Hoang, Nguyen Dinh, Rector, R. Blake

“…The primary goal of this paper is to present a unified approach and shed new light on convex and Clarke generalized differentiation theories using the concepts and techniques from Mordukhovich’s developments…”
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The Fermat rule for multifunctions on Banach spaces by Zheng, Xi Yin, Ng, Kung Fu

“… In particular, in terms of the coderivatives, we present Fermat's rules as necessary conditions for an optimal solution of the above problems…”
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Approximating Stationary Points of Stochastic Mathematical Programs with Equilibrium Constraints via Sample Averaging by Xu, Huifu, Ye, Jane J.

“…(Clarke)-stationary point of the sample average approximation problem to those of the true problem…”
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First order necessary optimality conditions for mathematical programs with second-order cone complementarity constraints by Zhang, Yi, Wu, Jia, Zhang, Liwei

“… Using the formulas of regular and limiting coderivatives and generalized Clarke’s Jacobian of the projection operator onto second-order cones from the literature, we present the S-, M-, C- and A-stationary conditions for a MPSCC problem…”
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Another characterization of convexity for set-valued maps by Sach, Pham Huu

“… It is established for a closed map F having nonconvex values. The main tool in this paper is the coderivative of F which is constructed with the help of an abstract subdifferential notion of Penot…”
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The Linear Nonconvex Generalized Gradient and Lagrange Multipliers by Treiman, Jay S.

“… The generalized gradient is the linear generalized gradient. It is smaller than the generalized gradients of Clarke and Mordukhovich but retains much of their nice calculus…”
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Generalized Jacobian for Functions with Infinite Dimensional Range and Domain by Páles, Zsolt, Zeidan, Vera

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