A line search filter sequential adaptive cubic regularisation algorithm for nonlinearly constrained optimization

TL;DR

This paper introduces a sequential adaptive cubic regularization algorithm with line search filters for solving nonlinear equality constrained optimization problems, improving constraint handling and convergence properties.

Contribution

It proposes a novel combination of adaptive cubic regularization with line search filter techniques for constrained optimization, enhancing efficiency and robustness.

Findings

Global convergence under mild assumptions

Effective constraint handling via composite step approach

Preliminary numerical results show promising performance

Abstract

In this paper, a sequential adaptive regularization algorithm using cubics (ARC) is presented to solve nonlinear equality constrained optimization. It is motivated by the idea of handling constraints in sequential quadratic programming methods. In each iteration, we decompose the new step into the sum of the normal step and the tangential step by using composite step approaches. Using a projective matrix, we transform the constrained ARC subproblem into a standard ARC subproblem which generates the tangential step. After the new step is computed, we employ line search filter techniques to generate the next iteration point. Line search filter techniques enable the algorithm to avoid the difficulty of choosing an appropriate penalty parameter in merit functions and the possibility of solving ARC subproblem many times in one iteration in ARC framework. Global convergence is analyzed under some mild assumptions. Preliminary numerical results and comparison are reported.