Professor Shaohua Pan was invited to give a lecture

发布时间: 2023-11-30 21:24:00

Topic： Calmness of partial perturbation to composite rank constraint systems and its applications to combinatorial optimization

Speaker：Shaohua Pan

Time：2023-11-29 15:00-16:00

Tencent Meeting ID： 656-4902-4546

Introduction：

    This talk concerns the calmness of a partial perturbation to the composite rank constraint system, an intersection of the rank constraint set and a general closed set, which is shown to be equivalent to a local Lipschitzian error bound and also a global Lipschitzianerror bound under a certain compactness condition, Based on its lifted formulation, we derive two criteria for identifying those closed sets such that the associated partial perturbation possesses the calmness, and provide a collection of examples to demonstrate that the criteria are satistied by common nonnegative and positive semidefinite rank constraint sets. Then, we apply the calmness of this class of partial perturbation to achieve several global exact penalties for rank constrained optimization, and employ one of them to propose a continuous relaxation approach to a class of unconstrained binary polynomial programs. Numerical tests on 184 instances demonstrate the efficiency of the proposed method, which can solve the problem of 20000 variables in $10$ minutes on an ordinary workstation and yields an upper bound to the best with a relative error at most 2.428%.

Organizer

School of Mathematical Sciences, South China Normal University, Machine Learning and Optimization Computing Laboratory

Co-organizers

Guangdong Young Scientists Association

Guangdong Computational Mathematical Society