Convergence of Symmetric Rank-One method based on Modified Quasi-Newton equation

Abstract

In this paper we investigate on convergence rate of a modified symmetric rank-one (SR1) method for unconstrainedoptimization problems. In general, the modified SR1 method incorporates a modified secant equationinto the standard SR1 method. Also a restart procedure is applied to avoid the loss of positive definiteness and zero denominator.A remarkable feature of the modified SR1 method is that it possesses at most $n+1$-step $q$-superlinearly convergent and$2n$-step quadratic convergent without uniformly independent assumptions of steps.