Results 41 to 50 of about 149 (133)
Sufficient optimality conditions and duality for nonsmooth multiobjective optimization problems via higher order strong convexity [PDF]
Yugoslav Journal of Operations Research, 2017 In this paper, we define some new generalizations of strongly convex functions of order m for locally Lipschitz functions using Clarke subdifferential.
Upadhyay Balendu B. +2 more
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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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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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Reconstruction of the Clarke Subdifferential by the Lasry–Lions Regularizations
Journal of Mathematical Analysis and Applications, 2000 Suppose that \(f\) is a locally Lipschitz function defined on a Hilbert space, which satisfies the growth condition \[ -{C\over 2}(\|x\|^2+ 1)\leq f(x)\leq {C\over 2}(\|x\|^2+ 1). \] It is proved that the Clarke subdifferential \(\partial f(x)\) (of \(f\) at \(x\)) can be represented by the derivatives of its Lasry-Lions regularizations \((f_\lambda ...
Georgiev, Pando Gr., Zlateva, Nadia P.
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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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Multivalued nonmonotone dynamic boundary condition
Boundary Value Problems, 2021 In this paper, we introduce a new class of hemivariational inequalities, called dynamic boundary hemivariational inequalities, reflecting the fact that the governing operator is also active on the boundary.
Khadija Aayadi +3 more
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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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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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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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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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