Convergence analysis of the self-dual optimally conditioned ssvm method of oren-spedicato

Abstract

This paper studies the convergence properties of the self-d ual optimally conditioned SSYM method of Oren-S pedicato [14] for unconstrained optimization. We show that the method with inexact line searches is globally convergent for general convex functions. Moreover, if we assume that the objective function f(x) is uniformly convex, then the iterates generated by the method convergeR-linearly to the solution and the search directions approach the Newton's direction asymptotically. Therefore, superlinear convergence would be obtained if the stepsize α_k is chosen appropriately. For example, the stepsize generated by exact line searches or by the strategy suggested by Nocedal and Yuan ([ I I] , P29) would guarantee superlincar convergence

Keywords:

• Self-scaling
• OS method
• Variable metric method
• Global convergence
• Superlinear convergence
• Unconstrained optimization