TY - JOUR

T1 - Superlinear and quadratic convergence of affine-scaling interior-point Newton methods for problems with simple bounds without strict complementarity assumption

AU - Heinkenschloss, Matthias

AU - Ulbrich, Michael

AU - Ulbrich, Stefan

PY - 1999/12

Y1 - 1999/12

N2 - A class of affine-scaling interior-point methods for bound constrained optimization problems is introduced which are locally q-superlinear or q-quadratic convergent. It is assumed that the strong second order sufficient optimality conditions at the solution are satisfied, but strict complementarity is not required. The methods are modifications of the affine-scaling interior-point Newton methods introduced by T. F. Coleman and Y. Li (Math. Programming, 67, 189-224, 1994). There are two modifications. One is a modification of the scaling matrix, the other one is the use of a projection of the step to maintain strict feasibility rather than a simple scaling of the step. A comprehensive local convergence analysis is given. A simple example is presented to illustrate the pitfalls of the original approach by Coleman and Li in the degenerate case and to demonstrate the performance of the fast converging modifications developed in this paper.

AB - A class of affine-scaling interior-point methods for bound constrained optimization problems is introduced which are locally q-superlinear or q-quadratic convergent. It is assumed that the strong second order sufficient optimality conditions at the solution are satisfied, but strict complementarity is not required. The methods are modifications of the affine-scaling interior-point Newton methods introduced by T. F. Coleman and Y. Li (Math. Programming, 67, 189-224, 1994). There are two modifications. One is a modification of the scaling matrix, the other one is the use of a projection of the step to maintain strict feasibility rather than a simple scaling of the step. A comprehensive local convergence analysis is given. A simple example is presented to illustrate the pitfalls of the original approach by Coleman and Li in the degenerate case and to demonstrate the performance of the fast converging modifications developed in this paper.

KW - Affine scaling

KW - Bound constraints

KW - Degeneracy

KW - Interior-point algorithms

KW - Nonlinear programming

KW - Optimality conditions

KW - Superlinear convergence

UR - http://www.scopus.com/inward/record.url?scp=0000860416&partnerID=8YFLogxK

U2 - 10.1007/s101070050107

DO - 10.1007/s101070050107

M3 - Article

AN - SCOPUS:0000860416

SN - 0025-5610

VL - 86

SP - 615

EP - 635

JO - Mathematical Programming

JF - Mathematical Programming

IS - 3

ER -