# A filter active-set trust-region method

M. P. Friedlander, N. I. M. Gould, S. Leyffer, T. S. Munson
Preprint ANL/MCS-P1456-0907, Argonne National Laboratory, 2007

## Abstract

We propose a two-phase active-set method for nonlinearly constrained optimization. The first phase solves a regularized linear program (LP) that serves to estimate an optimal active set. The second phase uses this active-set estimate to determine an equality-constrained quadratic program which provides for fast local convergence. A filter promotes global convergence. The regularization term in the first phase bounds the LP solution and plays role similar to an explicit ellipsoid trust-region constraint. We prove that the resulting method is globally convergent, and that an optimal active set is identified near a solution. We discuss alternative regularization functions that incorporate curvature information into the active-set identification phase. Preliminary numerical experiments on a subset of the CUTEr test problems illustrate the effectiveness of the approach.

## BiBTeX

@techreport{FrieGoulLeyfMuns:2007,
Author = {M. P. Friedlander and N. I. M. Gould and
S. Leyffer and T. S. Munson},
Institution = {Argonne National Laboratory},
Month = {September},
Number = {ANL/MCS-P1456-0907},
Title = {A filter active-set trust-region method},
Type = {Preprint},
Year = {2007}
}