A Successive Gap Constraint Linearization Method for Optimal Control Problems with Equilibrium Constraints

TL;DR

This paper introduces a new reformulation and a successive linearization method for optimal control problems with equilibrium constraints, improving efficiency and regularity for better solution strategies.

Contribution

It presents a novel gap-constraint reformulation that simplifies the constraint system and enhances differentiability, along with an efficient linearization method for solving discretized OCPECs.

Findings

Reformulation yields a more concise constraint system.

The method improves constraint regularity via relaxation.

Numerical experiments confirm effectiveness and efficiency.

Abstract

In this study, we propose a novel gap-constraint-based reformulation for optimal control problems with equilibrium constraints (OCPECs). We show that the proposed reformulation generates a new constraint system equivalent to the original one but more concise and with favorable differentiability. Moreover, constraint regularity can be recovered by a relaxation strategy. We show that the gap constraint and its gradient can be evaluated efficiently. We then propose a successive gap constraint linearization method to solve the discretized OCPEC. We also provide an intuitive geometric interpretation of the gap constraint. Numerical experiments validate the effectiveness of the proposed reformulation and solution method.