Document Type
Technical Report
Abstract
This paper studies a Mayer type optimal control problem with general endpoint constraints for semilinear unbounded evolution inclusions in reflexive and separable Banach spaces. First, we construct a sequence of discrete approximations to the original optimal control problem for evolution inclusions and prove that optimal solutions to discrete approximation problems uniformly converge to a given optimal solution for the original continuous-time problem. Then, based on advanced tools of generalized differentiation, we derive necessary optimality conditions for discrete-time problems under fairly general assumptions. Combining these results with recent achievements of variational analysis in infinite-dimensional spaces, we establish new necessary optimality conditions for constrained continuous-time evolution inclusions by passing to the limit from discrete approximations.
Number in Series
2004.11
Disciplines
Applied Mathematics | Mathematics
Recommended Citation
Mordukhovich, Boris S. and Wang, Dong, "Optimal Control of Semilinear Evolution Inclusions via Discrete Approximations" (2004). Mathematics Research Reports. 28.
https://digitalcommons.wayne.edu/math_reports/28
Comments
Dedicated to Czeslaw Olech. This research was partly supported by the National Science Foundation under grant DMS-0304989 and by the Australian Research Council under grant DP-0451168.