Work

Nonsmooth Composite Matrix Optimization: Strong Regularity, Constraint Nondegeneracy and Beyond

Year: 2019

Type: preprint

Abstract: The nonsmooth composite matrix optimization problem (CMatOP), in particular, the matrix norm minimization problem, is a generalization of the matrix conic programming problem with wide applications in numerical linear algebra, computational statistics and engineering. This paper is devoted to the characterization of the strong regularity for the CMatOP via the generalized strong second order sufficient condition and constraint nondegeneracy for problems with nonsmooth objective functions. The derived result supplements the existing characterization of the strong regularity for the constrained optimization problems with twice continuously differentiable data.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1907.13253

Authors: Cui, Ying, Ding, Chao

Institutions: University of Southern California, Chinese Academy of Sciences

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2966501932

Cites: 38

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Related to: 10