Document Type

Technical Report

Abstract

The paper is devoted to well-posed discrete approximations of the so-called generalized Bolza problem of minimizing variational functionals defined via extended-real-valued functions. This problem covers more conventional Bolza-type problems in the calculus of variations and optimal control of differential inclusions as well of parameterized differential equations. Our main goal is find efficient conditions ensuring an appropriate epi-convergence of discrete approximations, which plays a significant role in both the qualitative theory and numerical algorithms of optimization and optimal control. The paper seems to be the first attempt to study epi-convergent discretizations of the generalized Bolza problem; it establishes several rather general results in this direction.

Number in Series

2006.12

Disciplines

Applied Mathematics | Mathematics | Numerical Analysis and Computation

AMS Subject Classification

49M25, 90C99, 65L12

Comments

This research was partially supported by the USA National Science Foundation under grants DMS-0304989 and DMS-0603846, by the Australian Research Council under grant DP-0451168, and by the Finnish Academy of Sciences under contract No. 3385.

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