Abstract

In this paper we investigate on convergence rate of a modified symmetric rank-one (SR1) method for unconstrained
optimization problems. In general, the modified SR1 method incorporates a modified secant  equation
into 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.

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