Primal-dual nonlinear rescaling method with dynamic scaling parameter update

Authors:
Igor Griva;Roman A. Polyak
Affiliations:
Department of Mathematical Sciences, George Mason University, 22030, Fairfax, VA, USA;Department of SEOR and Mathematical Sciences Department, George Mason University, 22030, Fairfax, VA, USA
Venue:
Mathematical Programming: Series A and B
Year:
2006

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Abstract

In this paper we developed a general primal-dual nonlinear rescaling method with dynamic scaling parameter update (PDNRD) for convex optimization. We proved the global convergence, established 1.5-Q-superlinear rate of convergence under the standard second order optimality conditions. The PDNRD was numerically implemented and tested on a number of nonlinear problems from COPS and CUTE sets. We present numerical results, which strongly corroborate the theory.