主 講 人：葉明露
It is well known that the monotonicity of the underlying mapping of variational inequalities plays a central role in the convergence analysis. In this paper, we propose an infeasible projection algorithm (IPA for short) for nonmonotone variational inequalities. The next iteration point of IPA is generated by projecting a vector onto a half-space. Hence, the computational cost of computing the next iteration point of IPA is much less than the algorithm of Ye and He (2015) (YH for short). Moreover, if the underlying mapping is Lipschitz continuous with its modulus is known, by taking suitable parameters, IPA requires only one projection onto the feasible set per iteration. The global convergence of IPA is obtained when the solution set of its dual variational inequalities is nonempty. Moreover, if in addition error bound holds, the convergence rate of IPA is Q-linear. IPA can be used for quasi-monotone variational inequalities with its dual variational inequalities is nonempty. Comparing with YH by solving high-dimensional nonmonotone variational inequalities, numerical experiments show that IPA is much more efficient than YH both from CPU time point of view and the number of iterations point of view.
西華師范大學教授，碩士研究生導師。研究方向：非線性最優化，變分不等式投影算法，非凸優化問題的算法。2014年畢業于四川師范大學數學系，獲理學博士學位。2017年6月-2018年6月在香港理工大學跟隨Ting Kei Pong博士后做博士后研究。2011年至今在SIAM J. Optim., Comput. Optim. Appl., Optim., J. Oper. Res. Soc. China, 應用數學學報, 數學進展等期刊發表多篇論文。部分成果削弱了經典變分不等式投影算法對單調性的假設。