报告主题：求解结构优化的双分裂增广拉格朗日方法(An Two splitting augmented Lagrangian methods with partial quadratic approximation for structural optimization.)
报 告 人：简金宝 教授（广西民族大学）
报告时间：2021年6月10日（周四） 13:00
报告地点：校本部G507
邀请人：白延琴教授
报告摘要：In this talk, we focus on the two-block nonconvex and nonsmooth optimization with linear constraints, where the objective function is the sum of a convex but nonsmooth function and a smooth but nonconvex function. This problem encompasses many important applications in engineering and machine learning. Combining ideas from the splitting algorithm and making use of the quadratic approximation of the smooth part, with the help of Armijo line search technique, we first propose a splitting augmented Lagrangian method with partial quadratic approximation. Under some mild conditions, the global convergence of the proposed method is proved. Moreover, when the gradient of the smooth part in the objective function is Lipschitz continuous, we then propose and analyze a variant of the aforementioned method without performing line search. We report some preliminary numerical results on solving nonconvex quadratic regularization problems to show the feasibility and effectiveness of the two proposed methods. Finally, we show applicability and encouraging efficiency of our methods by applying them to solve sparse signal restoration problems.