Results 31 to 40 of about 2,296 (157)
Mathematics, 2022 This paper discusses optimality conditions for Borwein proper efficient solutions of nonsmooth multiobjective optimization problems with vanishing constraints. A new notion in terms of contingent cone and upper directional derivative is introduced, and a
Hui Huang, Haole Zhu
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On generalized derivatives for C1,1 vector optimization problems
Journal of Applied Mathematics, 2003 We introduce generalized definitions of Peano and Riemann directional derivatives in order to obtain second-order optimality conditions for vector optimization problems involving C1,1 data.
Davide La Torre
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KKT reformulation and necessary conditions for optimality in nonsmooth bilevel optimization [PDF]
, 2014 For a long time, the bilevel programming problem has essentially been considered as a special case of mathematical programs with equilibrium constraints (MPECs), in particular when the so-called KKT reformulation is in question.
Dempe, Stephan, Zemkoho, Alain B.
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Necessary optimality conditions for nonsmooth vector optimization problems
Mathematical Modelling and Analysis, 2003 In this paper we introduce a notion of generalized derivative for nonsmooth vector functions in order to obtain necessary optimality conditions for vector optimization problems.
Davide La Torre
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Optimizing condition numbers [PDF]
, 2009 In this paper we study the problem of minimizing condition numbers over a compact convex subset of the cone of symmetric positive semidefinite $n\times n$ matrices. We show that the condition number is a Clarke regular strongly pseudoconvex function.
Jane J. Ye, Lewis A.S., Pierre Maréchal
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Approximate controllability for second order nonlinear evolution hemivariational inequalities
Electronic Journal of Qualitative Theory of Differential Equations, 2016 The goal of this paper is to study approximate controllability for control systems driven by abstract second order nonlinear evolution hemivariational inequalities in Hilbert spaces.
Xiuwen Li +2 more
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Separable determination of integrability and minimality of the Clarke subdifferential mapping [PDF]
Proceedings of the American Mathematical Society, 1999 Frequently it is pointed out that the Clarke subdifferential of a Lipschitz function is too large to conclude about the structure of the associated function. In this manner, some years ago the authors presented large classes of functions (e.g., essentially smooth functions) for which their subdifferentials are well-behaved, i.e., they are \(D ...
Borwein, Jonathan M., Moors, Warren B.
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Abstract and Applied Analysis, 2003 The notions of relaxed submonotone and relaxed monotone mappings in Banach spaces are introduced and many of their properties are investigated. For example, the Clarke subdifferential of a locally Lipschitz function in a separable Banach space is relaxed
Tzanko Donchev, Pando Georgiev
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Viability problem with perturbation in Hilbert space
Electronic Journal of Qualitative Theory of Differential Equations, 2007 This paper deals with the existence result of viable solutions of the differential inclusion $$\dot{x}(t) \in f(t,x(t)) + F(x(t))$$ $$x(t) \in K \quad \text{on } [0,T],$$ where $K$ is a locally compact subset in separable Hilbert space $H,$ $(f(s,\cdot))
A. Ait, S. Sajid
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Hidden maximal monotonicity in evolutionary variational-hemivariational inequalities
Nonlinear Analysis, 2021 In this paper, we propose a new methodology to study evolutionary variational-hemivariational inequalities based on the theory of evolution equations governed by maximal monotone operators. More precisely, the proposed approach, based on a hidden maximal
Emilio Vilches, Shengda Zeng
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