题    目：Adaptive stepsize for Douglas-Rachford splitting algorithm and ADMM

主讲人：徐玲玲 副教授

单    位：南京师范大学

时    间：2024年11月10日 13:00

地    点：郑州校区九章学堂南楼C座302

摘    要：The Douglas-Rachford (DR) splitting algorithm is a classical first-order splitting algorithm for solving maximal monotone inclusion problems. We propose an adaptive stepsize for DR splitting algorithm (ADR), which sets the step size based on local information of the objective function, and only requires two extra function evaluations per iteration.We prove the global convergence of ADR and the sublinear convergence rate of the objective function value in the ergodic sense. In addition, we apply ADR to solve the dual problem of the separable convex optimization problem with linear equality constraints and obtain an alternating direction method of multipliers with line search (ADMM-LS). By demonstrating the relationship between ADR and ADMM-LS, we prove the global convergence of ADMM-LS. Finally, we test three numerical experiments to compare the ADR and ADMM-LS with other algorithms. The numerical results verify the effectiveness and efficiency of ADR and ADMM-LS.

简    介：徐玲玲，南京师范大学数学科学学院副教授，硕士生导师，主要从事最优化理论与算法方面的研究，主持国家自然科学基金青年基金、面上基金、江苏省高校自然科学基金等，另外主持科学与工程计算国家重点实验室开放课题(重点)一项，参加国家重点研发计划一项，担任中国运筹学会宣传委员会副主任、江苏省运筹学会常务副秘书长等职。