An interior point method for nonlinear optimization with a quasi-tangential subproblem

TL;DR

This paper introduces a novel interior point method for constrained nonlinear optimization that utilizes a quasi-tangential subproblem and a trust-funnel strategy, ensuring global convergence.

Contribution

It presents a new interior point algorithm with a quasi-tangential subproblem and a trust-funnel approach, advancing optimization techniques with proven convergence.

Findings

Global convergence under standard assumptions

Effective handling of null space constraints

Integration of trust-funnel strategy for globalization

Abstract

In this paper, we proposed an interior point method for constrained optimization, which is characterized by the using of quasi-tangential subproblem. This algorithm follows the main ideas of primal dual interior point methods and Byrd-Omojokun's step decomposition strategy. The quasi-tangential subproblem is obtained by penalizing the null space constraint in the tangential subproblem. The resulted quasi-tangential step is not strictly lying in the null space of the gradients of constraints. We also use a line search trust-funnel-like strategy, instead of penalty function or filter technology, to globalize the method. Global convergence results were obtained under standard assumptions.