Regularized Interior Point Methods for Constrained Optimization and Control

TL;DR

This paper introduces a novel algorithm that combines regularization and interior point methods for constrained nonlinear optimization, enhancing robustness and efficiency in control applications.

Contribution

It proposes a synergistic approach that integrates regularization with interior point methods, utilizing warm-starting and tailored subsolvers for improved performance.

Findings

The combined method shows superior robustness compared to traditional interior point and augmented Lagrangian methods.

Regularization improves linear algebra stability and convergence properties.

Numerical experiments demonstrate favorable performance in control-related optimization problems.

Abstract

Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an algorithm that synergistically combines them. Building a sequence of closely related subproblems and approximately solving each of them, this approach inherently exploits warm-starting, early termination, and the possibility to adopt subsolvers tailored to specific problem structures. Moreover, by relaxing the equality constraints with a proximal penalty, the regularized subproblems are feasible and satisfy a strong constraint qualification by construction, allowing the safe use of efficient solvers. We show how regularization benefits the underlying linear algebra and a detailed convergence analysis indicates that limit points tend to minimize constraint violation and satisfy suitable optimality conditions. Finally, we report on numerical results in terms of robustness, indicating that the combined approach compares favorably against both interior point and augmented Lagrangian codes.