2021/02/20 by Yitian Qian, Qian, Yitian, Shaohua Pan +3
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2102.10373
openalex publication_date 2021/02/20 · openalex created_date 2023/02/21 · openalex updated_date 2026/07/28
This paper is concerned with 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 Lipschitz-type error bound and also a global Lipschitz-type error bound under a certain compactness. 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 satisfied by common nonnegative and positive semidefinite rank constraint sets. Then, we use the calmness of this perturbation to obtain several global exact penalties for rank constrained optimization problems, and a family of equivalent DC surrogates for rank regularized problems.