A one perturbation variational principle and applications

Title: A one perturbation variational principle and applications
Creator: Borwein, Jonathan; Cheng, Lixin; Fabian, Marián; Revalski, Julian P.
Relation: Set-Valued and Variational Analysis: theory and applications Vol. 12, Issue 1-2, p. 49-60
Publisher Link: http://dx.doi.org/10.1023/B:SVAN.0000023400.92518.cb
Publisher: Springer
Resource Type: journal article
Date: 2004
Description: We study a variational principle in which there is one common perturbation function φ for every proper lower semicontinuous extended real-valued function f defined on a metric space X. Necessary and sufficient conditions are given in order for the perturbed function f + φ to attain its minimum. In the case of a separable Banach space we obtain a specific principle in which the common perturbation function is, in addition, also convex and Hadamard-like differentiable. This allows us to provide applications of the principle to differentiability of convex functions on separable and more general Banach spaces.
Subject: variational principle; well posed optimization problem; perturbed optimization problem; separable Banach space; weak Asplund space; Gâteaux differentiability space
Identifier: http://hdl.handle.net/1959.13/1046903
Identifier: uon:14704
Identifier: ISSN:1877-0533
Language: eng
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