报告主题：邻近点算法的紧的次线性收敛速率
报告人：杨俊锋 教授 （南京大学数学系）
报告时间：2019 年 11 月 6 日（周三）14:00
报告地点：校本部 G507
邀请人：徐姿
报告摘要： Tight sublinear convergence rate of the proximal point algorithm for maximal monotone inclusion problems is established based on the squared fixed point residual. By using the performance estimation framework, the tight sublinear convergence rate problem is written as an infinite dimensional nonconvex optimization problem, which is then equivalently reformulated as a finite dimensional semidefinite programming (SDP) problem. By solving the SDP, exact sublinear rate is computed numerically. Theoretically, by constructing a feasible solution to the dual SDP, an upper bound is obtained for the tight sublinear rate, and, on the other hand, an example in two dimensional space is constructed to provide a lower bound. The lower bound matches exactly the upper bound obtained from the dual SDP, which also coincides with the numerical rate computed. Hence, we have established the worst case sublinear convergence rate, which is tight in terms of both the order and the constants involved. This is a joint work with Prof. Guoyong Gu from Nanjing University.
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