Infinite Penalization for Optimal Control Problems: An infinite‐dimensional optimization method for constrained optimization problems

Abstract

We present results on a method for infinite dimensional constrained optimization problems. In particular, we are interested in state constrained optimal control problems and discuss an algorithm based on penalization and smoothing. The algorithm contains update rules for the penalty and the smoothing parameter that depend on the constraint violation. Theoretical as well as numerical results are given.

Exact penalization of terminal constraints for optimal control problems

“…Another approach to deal with this problem numerically is to approximate the non‐smooth penalty term by family of smooth functions. For problems with inequality constraints, this approach has been studied in and .…”

“…In [24], it is shown that this problem is equivalent to the problem The form (35) of the Neumann optimal boundary control problems allows to show an interesting result on the structure of the optimal controls: For initial states with velocity zero, that is, y 1 D 0, there exists an optimal control that is odd with respect to the midpoint of the time interval. More precisely, we have the following:…”

“…Assume that T > 2 is a natural number. There exists an optimal control u that solves (35) and is odd with respect to the point T =2 on OE0; T , that is…”