报 告 人：叶明露 教授(西华师范大学)
报告摘要：In this talk, we first present a modified double projection algorithm (MDPA for short) for solving variational inequality problems (VIP for short) without monotonicity. Comparing with the algorithm of Ye and He (2015), the new iterate point of MDPA is generated by projecting the current iterate point onto the intersection of the feasible set and only one half-space. Moreover, we construct a new half-space which can separate strictly the current iterate point from the solution set of its dual variational inequalities. By using this new half-space, we present an improved double projection algorithm (IMDPA) for solving VIP without monotonicity. The global convergence of the two new algorithms are proved, respectively, whenever the underlying mapping is continuous and the solution set of its dual variational inequality is nonempty. Numerical experiments show that IMDPA can accelerate MDPA for solving nonmonotone VIP from the total number of iterative point of view. Moreover, IMDPA is more efficient than Algorithm 1 in [Van, Dinh B., Manh, H D., Thanh, T T H.: A modified Solodov-Svaiter method for solving nonmonotone variational inequality problems. Numerical Algorithms. 1--20 (2022)] from the CPU time point of view and the total number of iterative point of view.
专家简介：叶明露，西华师范大学教授，硕士生导师，美国《Mathematical Review》评论员。在变分不等式的数值算法、非凸非光滑优化算法方面得到了一些结果。所得结果发表在SIAM Journal on Optimization, Computational Optimization and Applications, Numerical Algorithms，Optimization等期刊上。2023年获得南充市科技创新成果奖二等奖（1/2），主持四川省教育厅项目一项。参与国家自然科学基金面上项目四项。