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Variational Analysis in Non-reflexive Spaces and Applications to Control Problems with $L^1$ Perturbations

Borwein, Jonathan M. and Zhu, Qiji J. (1997) Variational Analysis in Non-reflexive Spaces and Applications to Control Problems with $L^1$ Perturbations. Nonlinear Analysis: Theory, Methods & Applications, 28 (5). pp. 889-915. ISSN 0362546X

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      Abstract

      We provide a refined sensitivity analysis for finite and infinite horizon control problems where in both cases the perturbation space is $L^1$. Our underlying technique relies on a recent sequential description of both the generalized gradient of Clarke and of the approximate $G$--subdifferential of functions defined on a smooth Banach space. We also show that the proximal limit formula for the generalized gradient and its $L^p$ analogue are direct consequences of these sequential formulas. Related characterizations of Lipschitzness of a function on a smooth space are given.

      Item Type: Article
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: weak-Hadamard subderivatives, Holder subderivatives, variational principles, smooth renorms, Clarke subdifferentials, G-subdifferentials, sensitivity analysis, control system, infinite horizon problems
      Subjects: 49-xx Calculus of variations and optimal control; optimization > 49Jxx Existence theories
      49-xx Calculus of variations and optimal control; optimization > 49Kxx Necessary conditions and sufficient conditions for optimality
      58-xx Global analysis, analysis on manifolds > 58Cxx Calculus on manifolds; nonlinear operators
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 17 Nov 2003
      Last Modified: 13 Jan 2015 17:12
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/78

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