Derivatives of orbital function and an extension of Berezin-Gel’fand’s theorem
Special Matrices, 2016 A generalization of a result of Berezin and Gel’fand in the context of Eaton triples is given. The generalization and its proof are Lie-theoretic free and requires some basic knowledge of nonsmooth analysis.
Tam Tin-Yau, Hill William C.
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The approximate and the Clarke subdifferentials can be different everywhere
Journal of Mathematical Analysis and Applications, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the Subdifferentials of Quasiconvex and Pseudoconvex Functions and Cyclic Monotonicity [PDF]
, 1999 The notions of cyclic quasimonotonicity and cyclic pseudomonotonicity are introduced. A classical result of convex analysis concerning the cyclic monotonicity of the (Fenchel–Moreau) subdifferential of a convex function is extended to corresponding ...
Daniilidis, Aris, Hadjisavvas, Nicolas
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Topological Properties of the Approximate Subdifferential [PDF]
, 1994 The approximate subdifferential introduced by Mordukhovich has attracted much attention in recent works on nonsmooth optimization. Potential advantages over other concepts of subdifferentiability might be related to its non-convexity.
René Henrion
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Strong Kuhn–Tucker conditions and constraint qualifications in locally Lipschitz multiobjective optimization problems [PDF]
, 2009 Multiobjective optimization problems, Constraint qualification, Necessary conditions for Pareto minimum, Lagrange multipliers, Clarke subdifferential, 90C29, 90C46,
B. Jiménez +3 more
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Lipschitz Functions with Maximal Clarke Subdifferentials Are Generic [PDF]
, 1998 . We show that on a separable Banach space most Lipschitz functions have maximal Clarke subdifferential mappings. In particular, the generic nonexpansive function has the dual unit ball as its Clarke subdifferential at every point.
Jonathan M. Borwein, Xianfu Wang
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Journal of Inequalities and ApplicationsThis paper investigates the optimality conditions and scalarization theorems for robust approximate solutions to semi-infinite vector equilibrium problems with data uncertainty in the constraints.
Shan Cai, Xiaoping Li
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The Subdifferentiability Properties of Typical Functions inC[0,1] [PDF]
, 1998 LetCdenote the Banach space of continuous real valued functions on [0,1] with the uniform norm; ∂aand ∂cfdenote the approximate subdifferential and Clarke subdifferential.
Wang, Xianfu
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Three nontrivial solutions for nonlocal anisotropic inclusions under nonresonance
Electronic Journal of Differential Equations, 2019 In this article, we study a pseudo-differential inclusion driven by a nonlocal anisotropic operator and a Clarke generalized subdifferential of a nonsmooth potential, which satisfies nonresonance conditions both at the origin and at infinity. We prove
Silvia Frassu +2 more
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Convergence of a time discretization for a nonlinear second-order inclusion [PDF]
, 2017 We study an abstract second order inclusion involving two nonlinear single-valued operators and a nonlinear multi-valued term. Our goal is to establish the existence of solutions to the problem by applying numerical scheme based on time discretization ...
Szafraniec, Paweł +7 more
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