Conic formulation of QPCCs applied to truly sparse QPs

Immanuel M. Bomze () and Bo Peng ()
Additional contact information
Immanuel M. Bomze: University of Vienna
Bo Peng: University of Vienna

Computational Optimization and Applications, 2023, vol. 84, issue 3, No 2, 703-735

Abstract: Abstract We study (nonconvex) quadratic optimization problems with complementarity constraints, establishing an exact completely positive reformulation under—apparently new—mild conditions involving only the constraints, not the objective. Moreover, we also give the conditions for strong conic duality between the obtained completely positive problem and its dual. Our approach is based on purely continuous models which avoid any branching or use of large constants in implementation. An application to pursuing interpretable sparse solutions of quadratic optimization problems is shown to satisfy our settings, and therefore we link quadratic problems with an exact sparsity term $$\Vert {{\mathsf {x}}}\Vert _0$$ ‖ x ‖ 0 to copositive optimization. The covered problem class includes sparse least-squares regression under linear constraints, for instance. Numerical comparisons between our method and other approximations are reported from the perspective of the objective function value.

Keywords: Copositive optimization; Conic relaxation; Quadratic optimization; Sparsity; Complementarity constraints (search for similar items in EconPapers)
Date: 2023
References: Add references at CitEc
Citations: Track citations by RSS feed

Downloads: (external link)
http://link.springer.com/10.1007/s10589-022-00440-5 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:84:y:2023:i:3:d:10.1007_s10589-022-00440-5

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

DOI: 10.1007/s10589-022-00440-5

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 ().