A penalty method for nonlinear programs with set exclusion constraints

Abstract

A common requirement in optimal control problems arising in autonomous navigation is that the decision variables are constrained to be outside certain sets. Such set exclusion constraints represent obstacles that must be avoided by the motion system. This paper presents a simple and efficient method for solving optimization problems with general set exclusion and implicit constraints. The method embeds the set exclusion constraints in a quadratic penalty framework and solves the inner optimization problems using a proximal algorithm that deals directly with the implicit constraints. We derive convergence results for this method by transforming the generated iterates to points of a reformulated problem with complementarity constraints. Furthermore, the practical application of the solution method is validated in numerical simulations of a model predictive control approach to path planning for a mobile robot. Finally, a runtime comparison with state-of-the-art solvers applied to the problem with complementarity constraints illustrates the efficiency of the proposed method.