Results 1 to 10 of about 108 (98)

Subdifferential Calculus Rules for Supremum Functions in Convex Analysis [PDF]

SIAM Journal on Optimization, 2011
Extending and improving some recent results of Hantoute, Lopez, and Zalinescu and others, we provide characterization conditions for subdifferential formulas to hold for the supremum function of a family of convex functions on a real locally convex space.
Chong Li, K F Ng
exaly   +2 more sources

Subdifferential calculus for a quasiconvex function with generator

Journal of Mathematical Analysis and Applications, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Daishi Kuroiwa
exaly   +2 more sources

Extensions of Fréchet ϵ-Subdifferential Calculus and Applications

Journal of Mathematical Analysis and Applications, 2002
AbstractIn this paper, we establish some calculus rules for the limiting Fréchet ϵ-subdifferentials of marginal functions and composite functions. Necessary conditions for approximate solutions of a constrained optimization problem are derived.
Huynh Van Ngai, Dinh The Luc, Michel Thera   +2 more
exaly   +2 more sources

Fréchet vector subdifferential calculus [PDF]

Carpathian Journal of Mathematics, 2020
In this paper, we study Fréchet vector subdifferentials of vector-valued functions in normed spaces which reduceto the known ones of extended-real-valued functions. We establish relations between two kinds of Fréchet vectorsubdifferentials and between subdifferential and coderivative; some of them improve the existing relations forextended-real-valued ...
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Subdifferential Calculus Using ϵ-Subdifferentials

Journal of Functional Analysis, 1993
AbstractIn applications of convex analysis it is important to be able to calculate the subdifferentials of various combinations of (proper and lower semicontinuous) convex functions, such as the sum of two such functions, or their inf-convolution ("epi-sum"), as well as the pre-composition of a convex function with an affine map or the "marginal ...
Hiriarturruty, J.B., Phelps, R.R.
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Calculus for Directional Limiting Normal Cones and Subdifferentials [PDF]

Set-Valued and Variational Analysis, 2018
The paper is devoted to the development of a comprehensive calculus for directional limiting normal cones, subdifferentials and coderivatives in finite dimensions. This calculus encompasses the whole range of the standard generalized differential calculus for (non-directional) limiting notions and relies on very weak (non-restrictive) qualification ...
Matúš, Benko, Gfrerer, Helmut, Outrata, Jiří V.   +2 more
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On nonconvex subdifferential calculus in binormed spaces [PDF]

International Mathematical Forum, 2007
We give in this paper some useful calculus results related to the limiting subdifferential in binormed spaces (generalized limiting subdifferential) which is a generalization of the limiting subdifferential in Banach spaces [5, 6].
S. Lahrech, J. Hlal, A. Ouahab, A. Jaddar, A. Mbarki   +4 more
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Geometric Approach to Subdifferential Calculus

, 2015
In this paper we develop a geometric approach to convex subdifferential calculus in finite dimensions with employing some ideas of modern variational analysis. This approach allows us to obtain natural and rather easy proofs of basic results of convex subdifferential calculus in full generality and also derive new results of convex analysis concerning ...
Mordukhovich, Boris, Nam, Nguyen Mau
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Convex regularization and subdifferential calculus

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
Abstract This paper deals with the regularization of the sum of functions defined on a locally convex space through their closed-convex hulls in the bidual space. Different conditions guaranteeing that the closed-convex hull of the sum is the sum of the corresponding closed-convex hulls are provided. These conditions are expressed in terms of
Rafael Correa, Abderrahim Hantoute, Marco A. López   +2 more
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The directed and Rubinov subdifferentials of quasidifferentiable functions, Part II: Calculus [PDF]

Nonlinear Analysis: Theory, Methods & Applications, 2012
We continue the study of the directed subdifferential for quasidifferentiable functions started in [R. Baier, E. Farkhi, V. Roshchina: The directed and Rubinov subdifferentials of quasidifferentiable functions, Part I: Definitions and examples, Nonlinear Anal., same volume].
Baier, Robert, Farkhi, Elza, Roshchina, Vera   +2 more
openaire   +1 more source