Accelerated inexact composite gradient methods for nonconvex spectral optimization problems

Weiwei Kong () and Renato D. C. Monteiro ()
Additional contact information
Weiwei Kong: Oak Ridge National Laboratory
Renato D. C. Monteiro: Georgia Institute of Technology

Computational Optimization and Applications, 2022, vol. 82, issue 3, No 5, 673-715

Abstract: Abstract This paper presents two inexact composite gradient methods, one inner accelerated and another doubly accelerated, for solving a class of nonconvex spectral composite optimization problems. More specifically, the objective function for these problems is of the form $$f_{1}+f_{2}+h$$ f 1 + f 2 + h , where $$f_{1}$$ f 1 and $$f_{2}$$ f 2 are differentiable nonconvex matrix functions with Lipschitz continuous gradients, $$h$$ h is a proper closed convex matrix function, and both $$f_{2}$$ f 2 and $$h$$ h can be expressed as functions that operate on the singular values of their inputs. The methods essentially use an accelerated composite gradient method to solve a sequence of proximal subproblems involving the linear approximation of $$f_{1}$$ f 1 and the singular value functions underlying $$f_{2}$$ f 2 and $$h$$ h . Unlike other composite gradient-based methods, the proposed methods take advantage of both the composite and spectral structure underlying the objective function in order to efficiently generate their solutions. Numerical experiments are presented to demonstrate the practicality of these methods on a set of real-world and randomly generated spectral optimization problems.

Keywords: Composite nonconvex problem; Iteration complexity; Inexact composite gradient method; First-order accelerated gradient method; Spectral optimization (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10589-022-00377-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:82:y:2022:i:3:d:10.1007_s10589-022-00377-9

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-022-00377-9

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().