On Superlinear Convergence of Infeasible Interior-PointAlgorithms for Linearly Constrained Convex Programs

Authors:
Renato D. C. Monteiro;Fangjun Zhou
Affiliations:
School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332. E-mail: monteiro@isye.gatech.edu;School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332. E-mail: monteiro@isye.gatech.edu
Venue:
Computational Optimization and Applications
Year:
1997

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Abstract

This note derives bounds on the length of the primal-dual affinescaling directions associated with a linearly constrained convexprogram satisfying the following conditions: 1) the problem has asolution satisfying strict complementarity, 2) the Hessian of theobjective function satisfies a certain invariance property. Weillustrate the usefulness of these bounds by establishing thesuperlinear convergence of the algorithm presented in Wright andRalph [22] for solving the optimality conditions associatedwith a linearly constrained convex program satisfying the aboveconditions.