Results 171 to 180 of about 2,743 (188)

Tangent cone and contingent cone to the intersection of two closed sets

Nonlinear Analysis: Theory, Methods & Applications, 2010
Let \(X\) be a normed vector space and \(C\subset X\) a nonempty closed set; let \(T_C(x)\) denote the tangent cone to \(C\) at \(x\in C\). For \(X=\mathbb R^n\), \textit{R. T. Rockafellar} [Nonlinear Anal., Theory Methods Appl.\ 3, 145--154 (1979; Zbl 0443.26010)] has shown that, if \(x\in C_1\cap C_2\), then \[ T_{C_1}(x)\cap T_{C_2}(x)\subset T_{C_1\
Zili Wu
exaly   +2 more sources

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.
Xinmin Yang, Zhi-Ang Zhou, Yang Xin-Min   +2 more
exaly   +2 more sources

Sliding mode control design via piecewise smooth Lipschitz surfaces based on contingent cone criteria

International Journal of Control, Automation and Systems, 2014
In order to improve flexibility of sliding mode control (SMC) for a class of nonlinear systems, a new control design method is proposed in this paper. The sliding surface is extended to be a generic Lipschitz continuous surface instead of a smooth one, with which different characteristics of sliding motion may be realized.
Kai Zheng, Xin Huo, Ma Kemao
exaly   +2 more sources

Cone-directed contingent derivatives and generalized preinvex set-valued optimization

Acta Mathematica Scientia, 2007
Abstract By using cone-directed contingent derivatives, the unified necessary and sufficient optimality conditions are given for weakly and strongly minimal elements respectively in generalized preinvex set-valued optimization.
exaly   +2 more sources

About contingent epiderivatives [PDF]

Journal of Mathematical Analysis and Applications, 2007
In this paper we analyze some questions concerning the contingent epiderivative. When the ordering cone is not necessarily pointed we introduce the notion of family of contingent epiderivatives. We also investigate the relationship between the contingent
MIGUEL Sama, Luis Rodríguez-Marín
exaly   +2 more sources

On the intersection of contingent cones

Journal of Optimization Theory and Applications, 1991
A new condition that ensures the equality \[ (1)\quad T_{K\cap L}(x)=T_ K(x)\cap T_ L(x),\quad x\in K\cap L, \] \[ T_ K(x)=\{v\in X| \quad \liminf_{h\downarrow 0+}[dist(K,x+hv)/h]=0\} \] for convex closed subsets K, L of a Hilbert space X is established.
openaire   +2 more sources

Corrigendum to "Convex Subcones of the Contingent Cone in Nonsmooth Calculus and Optimization"

Transactions of the American Mathematical Society, 1989
This is a correction to the paper ibid. 302, 661-682 (1987; Zbl 0629.58007).
openaire   +1 more source

OPTIMALITY OF GLOBAL PROPER EFFICIENCY FOR CONE-ARCWISE CONNECTED SET-VALUED OPTIMIZATION USING CONTINGENT EPIDERIVATIVE

Asia-Pacific Journal of Operational Research, 2013
This note deals with the optimality conditions of set-valued unconstraint optimization problem in real normed linear spaces. Based upon the concept of contingent epiderivative, the unified necessary and sufficient optimality conditions for global proper efficiency in vector optimization problem involving cone-arcwise connected set-valued mapping are ...
openaire   +3 more sources

On Constrained Set-Valued Semi-Infinite Programming Problems with ρ-Cone Arcwise Connectedness

Axioms, 2021
Savin Treanţă, , Das Koushik
exaly  

Cone arcwise connectivity in optimization problems with difference of set-valued mappings

SeMA Journal, 2023
Savin Treanţă, , Izhar Ahmad
exaly