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  • 数理基础与前沿研究论坛- A Peaceman-Rachford splitting method with monotone plus skew-symmetric splitting for nonlinear saddle point problems


    报告题目:A Peaceman-Rachford splitting method with monotone plus skew-symmetric splitting for nonlinear saddle point problems

    报告人:张文星副教授(电子科技大学)

    报告时间:20191206日(星期五)16:00-17:00

    报告地点:理学院三楼会议室(SL310)

    报告摘要

    This talk is devoted to solving the linearly constrained convex optimization problems by Peaceman-Rachford splitting method with monotone plus skew-symmetric splitting on KKT operators. This approach generalizes the Hermitian and skew-Hermitian splitting method, an unconditionally convergent algorithm for non-Hermitian positive definite linear systems, to the nonlinear scenario. The convergence of the proposed algorithm is guaranteed under some mild assumptions, e.g., the strict convexity on objective functions and the consistency on constraints, even though the Lions-Mercier property is not fulfilled. In addition, we explore an inexact version of the proposed algorithm, which allows solving the subproblems approximately with some inexactness criteria.  Numerical simulations on an image restoration problem demonstrate the compelling performance of the proposed algorithm.

    报告人简介:

    张文星, 2012年博士毕业于南京大学数学系,现为电子科技大学数学科学学院副教授。2014-2015年在法国图卢兹大学从事博士后研究。曾先后访问香港大学、香港中文大学、香港浸会大学等高校。主要研究兴趣为最优化理论与算法、变分不等式及应用。2017年入选四川省学术和技术带头人后备人选。主持国家自然科学面上项目一项。在Mathematics of Computation, Inverse Problems, SIAM Journal on Imaging Sciences, Journal of Scientific Computing, IEEE Trans Medical Imaging, IEEE Trans Image Process, Comput Optim Appl等杂志发表论论文20余篇。

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                  理学院

                 2019年12月1日