报告题目：A Globalized Semismooth Newton Method for Prox-regular Optimization Problems

报  告 人：吴育洽助理教授（深圳大学）

报告时间：2026年9月21日（周一）上午9:00-10:00

报告地点：广东工业大学龙洞校区行政楼610

报告摘要: We study a class of nonconvex and nonsmooth composite optimization problems with a twice continuously differentiable function and a prox-regular regularizer. Residual-based semismooth Newton methods require a single-valued, locally Lipschitz forward-backward residual, a property not directly guaranteed by ordinary prox-regularity at nonstationary iterates. We prove that this property holds for every sufficiently small proximal parameter. Building on this result, we develop a globalized semismooth Newton method safeguarded by proximal-gradient steps. We show that the whole sequence converges to an \(L\)-stationary point under a Kurdyka--\L ojasiewicz exponent condition, and establish a local superlinear rate under metric subregularity of the forward-backward residual, an inverse bound for the regularized Newton matrices, and a \((b)\)-regularity condition for the Clarke generalized Jacobian approximation. Numerical experiments demonstrate computational effectiveness.

报告人简介：吴育洽，深圳大学数学科学学院助理教授，研究方向为最优化理论与算法，专注于大规模非凸非光滑优化问题的二阶算法设计，研究成果发表于SIAM Journal on Optimization、Journal of Machine Learning Research等期刊上。主持国家青年科学基金项目（C类），入选首届中国运筹学会青年人才托举工程。