School of Mathematical Sciences Academic Report [2025] 055  

(High-Level University Construction Series Report No. 1077)  

Lecture Title: An extended sequential quadratic method with extrapolation  

Speaker: Assoc. Prof. Yongle Zhang (Sichuan Normal University)  

Date & Time: 4:00 PM – 5:30 PM, June 29, 2025  

Venue: Room 514, Convergence Stars Building  

Abstract: 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.

Biography: Yongle Zhang, Ph.D., Associate Professor and Master’s Supervisor at Sichuan Normal University, is recognized as a High-Level Overseas Talented Scholar by Sichuan Province and serves as a Reviewer for Mathematical Reviews. His research focuses on non-convex non-smooth optimization and variational inequalities, with 16 SCI-indexed publications in Mathematical Programming, Advances in Computational Mathematics, Journal of Optimization Theory and Applications, and Numerical Algorithms. He leads one NSFC Youth Program and one Sichuan Provincial Applied Basic Research Project. His courses Mathematical Modeling (National First-Class Undergraduate Course) and Ordinary Differential Equations (Sichuan Provincial First-Class Undergraduate Course) received national/provincial recognition.  

All faculty and students are welcome to attend!  

Invited by: Kai Tu  

School of Mathematical Sciences  

June 24, 2025