Implicit Euler approximation and optimization of one-sided Lipschitzian differential inclusions

This paper concerns the study of the generalized Bolza problem governed by differential inclusions satisfying the so-called “relaxed one-sided Lipschitzian” (ROSL) condition with respect to the state variables subject to various types of nonsmooth endpoint constraints. We construct discrete approxim...

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Bibliographic Details
Published inNonlinear Analysis and Optimization Vol. 659; pp. 165 - 188
Main Authors Mordukhovich, Boris S., Tian, Yuan
Format Book Chapter
LanguageEnglish
Published Providence, Rhode Island American Mathematical Society 24.02.2016
SeriesContemporary Mathematics
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ISBN9781470417369
1470417367
ISSN0271-4132
1098-3627
DOI10.1090/conm/659/13152

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Summary:This paper concerns the study of the generalized Bolza problem governed by differential inclusions satisfying the so-called “relaxed one-sided Lipschitzian” (ROSL) condition with respect to the state variables subject to various types of nonsmooth endpoint constraints. We construct discrete approximations of differential inclusions with ROSL right-hand sides by using the implicit Euler scheme for approximating time derivatives, and then we justify an appropriate well-posedness of such approximations. Our principal result establishes the uniform approximation of strong local minimizers for the continuous-time Bolza problem by optimal solutions to the implicitly discretized finite-difference systems in the general ROSL setting and even by the strengthen
ISBN:9781470417369
1470417367
ISSN:0271-4132
1098-3627
DOI:10.1090/conm/659/13152