A SUPERLINEARLY CONVERGENT METHOD TO LINEARLY CONSTRAINED OPTIMIZATION PROBLEMS UNDER DEGENERACY

Most papers concerning nonlinear programming problems with linear constraints assume linearindependence of the gradients of the active constraints at any feasible point.In this paper we removethis assumption and give an algorithm and prove its convergency.Also,under appropriate assump-tions on the objective function,including one which could be viewed as an extension of the strictcomplementary slackness condition at the optimal solution,we prove the rate of convergence of thealgorithm to be superlinear.