Composite-Step Like Filter Methods for Equality Constraint Problems

Abstract

  In a composite-step approach, a step $s_k$ is computed as the sum of two components $v_k$ and $h_k$. The normal component $v_k$, which is called the vertical step, aims to improve the linearized feasibility, while the tangential compoent $h_k$, which is also called horizontal step, concentrates on reducing a model of the merit functions. As a filter method, it reduces both the infeasibility and the objective function. This is the same property of these two methods. In this paper, one concerns the composite-step like filter approach. That is, a step is tangential component $h_k$ if the infeasibility is reduced. Or else, $s_k$ is a composite step composed of normal component $v_k$ and tangential component $h_k$.