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A one perturbation variational principle and applications

Borwein, Jonathan M. and Fabian, Marian and Revalski, Julian (2004) A one perturbation variational principle and applications. Set-Valued Analysis, 12 (1-2). pp. 49-60. ISSN 0927-6947

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      Abstract

      We study a variational principle in which there is one common perturbation function $\vv$ 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 $f+\vv$ 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.

      Item Type: Article
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: variational principle, well-posed optimization problem, perturbed optimization problem, separable Banach space, weak Asplund space, Gateaux differentiability space
      Subjects: 49-xx Calculus of variations and optimal control; optimization > 49Jxx Existence theories
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 27 Oct 2003
      Last Modified: 12 Jan 2015 15:17
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/14

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