A Vectorized Positive Semidefinite Penalty Method for Unconstrained Binary Quadratic Programming

Xinyue Huo () and Ran Gu ()
Additional contact information
Xinyue Huo: LPMC, KLMDASR and LEBPS, Nankai University
Ran Gu: LPMC, KLMDASR and LEBPS, Nankai University

Journal of Optimization Theory and Applications, 2026, vol. 208, issue 1, No 53, 31 pages

Abstract: Abstract The unconstrained binary quadratic programming (UBQP) problem is a class of problems of significant importance in many practical applications, such as in combinatorial optimization, circuit design, and other fields. The positive semidefinite penalty (PSDP) method originated from research on semidefinite relaxation, where the introduction of an exact penalty function improves the efficiency and accuracy of problem solving. In this paper, we propose a vectorized PSDP method for solving the UBQP problem, which optimizes computational efficiency by vectorizing matrix variables within a PSDP framework. Algorithmic enhancements in penalty updating and initialization are implemented, along with the introduction of two algorithms that integrate the proximal point algorithm and the projection alternating BB method for subproblem resolution. Properties of the penalty function and algorithm convergence are analyzed. Numerical experiments show the superior performance of the method in providing high-quality solutions and satisfactory solution times compared to the semidefinite relaxation method and other established methods.

Keywords: Binary quadratic programming; Positive semidefinite penalty function; Proximal point algorithm; Projection alternating BB stepsize; 65K05; 90C09; 90C20 (search for similar items in EconPapers)
Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-025-02883-2 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:joptap:v:208:y:2026:i:1:d:10.1007_s10957-025-02883-2

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-025-02883-2

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

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