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论文类型：期刊论文

发表时间：2018-08-01

发表刊物：ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH

收录刊物：SCIE

卷号：35

期号：4

ISSN号：0217-5959

关键字：Redistributed bundle method; subgradient; generalized variational inequality problem; zero point of operator; auxiliary problem principle; gap function

摘要：Based on the redistributed technique of bundle methods and the auxiliary problem principle, we present a redistributed bundle method for solving a generalized variational inequality problem which consists of finding a zero point of the sum of two multivalued operators. The considered problem involves a nonsmooth nonconvex function which is difficult to approximate by workable functions. By imitating the properties of lower-C-2 functions, we consider approximating the local convexification of the nonconvex function, and the local convexification parameter is modified dynamically in order to make the augmented function produce nonnegative linearization errors. The convergence of the proposed algorithm is discussed when the sequence of stepsizes converges to zero, any weak limit point of the sequence of serious steps x(k) is a solution of problem (P) under some conditions. The presented method is the generalization of the convex bundle method [Salmon, G, JJ Strodiot and VH Nguyen (2004). A bundle method for solving variational inequalities. SIAM Journal on Optimization, 14(3), 869-893].