Global convergence properties of two modified BFGS-type methods
This article studies a modified BFGS algorithm for solving smooth unconstrained strongly convex minimization problem. The modified BFGS method is based on the new quasi-Newton equation Bk+1sk=yk where yk*, =yk + Aksk andA k is a matrix. Wei, Li and Qi [WLQ] have proven that the average performance of two of those algorithms is better than that of the classical one. In this paper, we prove the global convergence of these algorithms associated to a general line search rule.
AMS Mathematics Subject Classification65H10 65F10
Key words and phrasesUnconstrained programme BFGS algorithm global convergence quasi-Newton method
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