Calmness of partial perturbation to composite rank constraint systems and its applications

Yitian Qian, Shaohua Pan () and Yulan Liu ()
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Yitian Qian: South China University of Technology
Shaohua Pan: South China University of Technology
Yulan Liu: Guangdong University of Technology

Journal of Global Optimization, 2023, vol. 85, issue 4, No 4, 867-889

Abstract: Abstract 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.

Keywords: Composite rank constraint systems; Calmness; Error bound; Exact penalty; 90C31; 54C60; 49K40 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-022-01239-8

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