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R-Linear Convergence of Limited Memory Steepest Descent

Frank E. Curtis(frank.e.curtis***at***gmail.com)
Wei Guo(weg411***at***lehigh.edu)

Abstract: The limited memory steepest descent method (LMSD) proposed by Fletcher is an extension of the Barzilai-Borwein “two-point step size” strategy for steepest descent methods for solving unconstrained optimization problems. It is known that the Barzilai-Borwein strategy yields a method with an R-linear rate of convergence when it is employed to minimize a strongly convex quadratic. This paper extends this analysis for LMSD, also for strongly convex quadratics. In particular, it is shown that the method is R-linearly convergent for any choice of the history length parameter. The results of numerical experiments are provided to illustrate behaviors of the method that are revealed through the theoretical analysis.

Keywords: unconstrained optimization; steepest descent methods; Barzilai-Borwein methods; limited memory methods; quadratic optimization; R-linear rate of convergence

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Unconstrained Optimization )

Citation: ISE/COR@L Technical Report 16T-010, Lehigh University, Bethlehem, PA, USA

Download: [PDF]

Entry Submitted: 10/12/2016
Entry Accepted: 10/12/2016
Entry Last Modified: 10/12/2016

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