报告题目：Variational characterizations of the D-gap function for a variational inequality problem

主讲人：李明华教授（重庆文理学院）

时间：2025年7月4日（周五）16:00 p.m.

地点：北院卓远楼305会议室

主办单位：统计与数学学院

摘要：In this talk, by virtue of a unified framework, we establish the formulas of subderivative, Clarke directional derivative, regular subdifferential, limiting subdifferential and Clarke subdifferential of a D-gap function for a variational inequality problem. Employing these formulas, we study the regularity of the D-gap function. Moreover, we provide some sufficient conditions of the KL inequality for the D-gap function. Especially, we give a sufficient and necessary condition of the KL inequality for the D-gap function when the reference point is a solution of the variational inequality problem. Finally, under the KL inequality of the D-gap function and being due to these formulas again, we show that a derivative-free descent method is globally convergent and has linear convergence rate.

主讲人简介：

李明华，重庆大学博士，现任重庆文理学院数学与人工智能学院副院长，教授，统计优化与复杂数据重庆市重点实验室主任，中国运筹学会数学规划分会青年理事。主要研究方向：最优化理论、算法及应用。主持国家自然科学基金2项，省部级自然基金4项。