Inspired and motivated by results of Bnouhachem et al. (Hacet. J. Math. Stat. 41(1):103-117, 2012), we propose a new modified LQP method by using a new optimal step size, where the underlying function F is co-coercive. Under some mild conditions, we show that the method is globally convergent. Some preliminary computational results are given to illustrate the efficiency of the proposed method.
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