Exact Penalty Functions for Optimal Control Problems I: Main Theorem and Free-Endpoint Problems

24 Jul 2019 Dolgopolik M. V. Fominyh A. V.

In this two-part study we develop a general approach to the design and analysis of exact penalty functions for various optimal control problems, including problems with terminal and state constraints, problems involving differential inclusions, as well as optimal control problems for linear evolution equations. This approach allows one to simplify an optimal control problem by removing some (or all) constraints of this problem with the use of an exact penalty function, thus allowing one to reduce optimal control problems to equivalent variational problems, apply numerical methods for solving, e.g. problems without state constraints, to problems including such constraints, etc... (read more)

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