A Matrix-free Algorithm for Equality Constrained Optimization Problems with Rank-deficient Jacobians

Frank E. Curtis(fecurtgmail.com)
Jorge Nocedal(nocedaleecs.northwestern.edu)
Andreas Waechter(andreaswwatson.ibm.com)

Abstract: We present a line search algorithm for large-scale equality constrained optimization designed primarily for problems with (near) rank-deficient Jacobian matrices. The method is matrix-free (i.e., it does not require explicit representations or factorizations of derivative matrices), allows for inexact step computations, and does not require inertia information in order to solve nonconvex problems. The main components of the approach are a trust region subproblem for handling ill-conditioned or inconsistent linear models of the constraints and a process for attaining a sufficient reduction in a local model of a penalty function for the complete primal-dual step. We show that the algorithm is globally convergent to first-order optimal points or to stationary points of an infeasibility measure. Numerical results are presented.

Keywords: large-scale optimization, constrained optimization, nonconvex programming, trust regions, inexact linear system solvers, Krylov subspace methods

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 2: Infinite Dimensional Optimization (Other )

Citation: submitted to SIAM Journal on Optimization

Download: [PDF]

Entry Submitted: 05/20/2008
Entry Accepted: 05/20/2008
Entry Last Modified: 05/20/2008

Modify/Update this entry