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
Applied Mathematics | Mathematics | Numerical Analysis and Computation
AMS Subject Classification
49M25, 90C99, 65L12
Mordukhovich, Boris S. and Pennanen, Teemu, "Epi-Convergent Discretization of the Generalizaed Bolza Problem in Dynamic Optimization" (2006). Mathematics Research Reports. 41.