爱情岛论坛 学术报告[2025] 055号

(高水平大学建设系列报告1077号)

报告题目: An extended sequential quadratic method with extrapolation

报告人：张永乐 副教授（四川师范大学）

报告时间：2025年6月29日 16:00-17:30

讲座地点：汇星楼514

报告内容：We revisit and adapt the extended sequential quadratic method (ESQM) for solving a class of difference-of-convex optimization problems whose constraints are defined as the intersection of level sets of Lipschitz differentiable functions and a simple compact convex set. Particularly, for this class of problems, we develop a variant of ESQM, called ESQM with extrapolation (ESQMe), which incorporates Nesterov's extrapolation techniques for empirical acceleration. Under standard constraint qualifications, we show that the sequence generated by ESQMe clusters at a critical point if the extrapolation parameters are uniformly bounded above by a certain threshold. Convergence of the whole sequence and the convergence rate are established by assuming Kurdyka-Lojasiewicz (KL) property of a suitable potential function and imposing additional differentiability assumptions on the objective and constraint functions. In addition, when the objective and constraint functions are all convex, we show that linear convergence can be established if a certain exact penalty function is known to be a KL function with exponent 1/2; we also discuss how the KL exponent of such an exact penalty function can be deduced from that of the original extended objective (i.e., sum of the objective and the indicator function of the constraint set). Finally, we perform numerical experiments to demonstrate the empirical acceleration of ESQMe over a basic version of ESQM, and illustrate its effectiveness by comparing with the natural competing algorithm SCPls.

报告人简历： 张永乐，博士，四川师范大学爱情岛论坛 副教授，硕士生导师，四川省海外高层次留学人才，美国数学评论评论员。主要从事非凸非光滑优化、变分不等式理论及算法的研究，在Mathematical Programming、Advances in Computational Mathematics、Journal of Optimization Theory and Applications、Numerical Algorithms等杂志上发表SCI索引论文16篇。主持国家自然科学基金青年科学基金1项、四川省科技厅应用基础项目1项。主讲的《数学建模》获评国家级一流本科课程，《常微分方程》入选四川省一流本科课程。

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