An accelerated active-set algorithm for a quadratic semidefinite program with general constraints

Chungen Shen (), Yunlong Wang, Wenjuan Xue and Lei-Hong Zhang ()
Additional contact information
Chungen Shen: University of Shanghai for Science and Technology
Yunlong Wang: Shanghai Jiao Tong University
Wenjuan Xue: Shanghai University of Electric Power
Lei-Hong Zhang: Soochow University

Computational Optimization and Applications, 2021, vol. 78, issue 1, No 1, 42 pages

Abstract: Abstract In this paper, we are concerned with efficient algorithms for solving the least squares semidefinite programming which contains many equalities and inequalities constraints. Our proposed method is built upon its dual formulation and is a type of active-set approach. In particular, by exploiting the nonnegative constraints in the dual form, our method first uses the information from the Barzlai–Borwein step to estimate the active/inactive sets, and within an adaptive framework, it then accelerates the convergence by switching the L-BFGS iteration and the semi-smooth Newton iteration dynamically. We show the global convergence under mild conditions, and furthermore, the local quadratic convergence under the additional nondegeneracy condition. Various types of synthetic as well as real-world examples are tested, and preliminary but promising numerical experiments are reported.

Keywords: Semidefinite programs; Active set; Barzlai–Borwein step; L-BFGS; Semi-smooth Newton; 65K05; 95C55; 90C30 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10589-020-00228-5 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:78:y:2021:i:1:d:10.1007_s10589-020-00228-5

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

DOI: 10.1007/s10589-020-00228-5

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 ().