A globally convergent regularized interior point method for constrained optimization

Abstract

This paper proposes a globally convergent regularized interior point method that involves a specifically designed regularization strategy for constrained optimization. The main concept of the proposed algorithm is that when a proper regularization parameter is selected, the direction obtained from the regularized barrier equation is a descent direction for either the objective function or constraint violation. Accordingly, by embedding a flexible strategy of choosing a regularization parameter in a trust-funnel-like interior point scheme, we propose the new algorithm. Global convergence under the mild assumptions of relaxed constant rank constraint qualification (RCRCQ) and local consistency of the linearized active and equality constraints is shown. Preliminary numerical experiments are conducted, and the results are encouraging.