报告题目：Error bound and exact penalty method for optimization problems with nonnegative orthogonal constraint

报告人：潘少华教授  华南理工大学数学学院

报告时间：2022年9月29日10：00

报告地点：龙洞校区行政楼610

主持人：常静雅

报告摘要：We concerned with a class of optimization problems with the nonnegative orthogonal constraint, in which the objective function is L-smooth on an open set containing the Stiefel manifold St(n,r). We derive a locally Lipschitzian error bound for the feasible points without zero rows when n>r>1, and when n>r=1 or n=r achieve a global Lipschitzian error bound. Then, we show that the penalty problem induced by the elementwise l-norm distance to the nonnegative cone is a global exact penalty, and so is the one induced by its Moreau envelope under a lower second-order calmness of the objective function. A practical penalty algorithm is developed by solving approximately a series of smooth penalty problems with a retraction-based nonmonotone line-search proximal gradient method, and any cluster point of the generated sequence is shown to be a stationary point of the original problem. Numerical comparisons with the ALM and the exact penalty method  indicate that our penalty method has an advantage in terms of the quality of solutions despite taking a little more time。

专家简介: 潘少华，华南理工大学数学学院教授、博士生导师。现任中国运筹学会理事和中国运筹学会数学规划分会常务理事。研究方向：锥约束优化及互补问题、低秩稀疏优化、结构非凸非光滑优化问题的理论与算法研究；主持国家自科基金和广东省自科基金各2项；在国内外重要刊物如Mathematical Programming, SIAM Journal on Optimization, SIAM Journal on Control and Optimization, Computational Optimization and Applications 等杂志发表论文50余篇。2019年荣获广东省自然科学奖二等奖。