On the Equivalence of Some Basic Principles in Variational Analysis

Borwein, Jonathan M. and Mordukhovich, Boris S. and Shao, Yongheng (1999) On the Equivalence of Some Basic Principles in Variational Analysis. Journal of Mathematical Analysis and Applications., 229 (1). pp. 228-257. ISSN 0022-247X

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      The primary goal of this paper is to study relationships between certain basic principles of variational analysis and its applications to nonsmooth calculus and optimization. Considering a broad class of Banach spaces admitting smooth renorms with respect to some bornology, we establish an equivalence between useful versions of a smooth variational principle for lower semicontinuous functions, an extremal principle for nonconvex sets, and an enhanced fuzzy sum rule formulated in terms of viscosity normals and subgradients with controlled ranks. Further refinements of the equivalence result are obtained in the case of a Fréchet differentiable norm. Based on the new enhanced sum rule, we provide a simplified proof for the refined sequential description of approximate normals and subgradients in smooth spaces.

      Item Type: Article
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: nonsmooth analysis, smooth Banach spaces, variational and extremal principles, generalized differentiation, fuzzy calculus, viscosity normals and subdifferentials
      Subjects: 49-xx Calculus of variations and optimal control; optimization > 49Jxx Existence theories
      46-xx Functional analysis > 46Bxx Normed linear spaces and Banach spaces; Banach lattices
      58-xx Global analysis, analysis on manifolds > 58Cxx Calculus on manifolds; nonlinear operators
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 28 Nov 2003
      Last Modified: 20 Sep 2014 15:22

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