Strong duality and minimal representations for cone optimization

Levent Tunçel and Henry Wolkowicz ()

Computational Optimization and Applications, 2012, vol. 53, issue 2, 619-648

Abstract: The elegant theoretical results for strong duality and strict complementarity for linear programming, LP, lie behind the success of current algorithms. In addition, preprocessing is an essential step for efficiency in both simplex type and interior-point methods. However, the theory and preprocessing techniques can fail for cone programming over nonpolyhedral cones. We take a fresh look at known and new results for duality, optimality, constraint qualifications, CQ, and strict complementarity, for linear cone optimization problems in finite dimensions. One theme is the notion of minimal representation of the cone and the constraints. This provides a framework for preprocessing cone optimization problems in order to avoid both the theoretical and numerical difficulties that arise due to the (near) loss of the strong CQ, strict feasibility. We include results and examples on the surprising theoretical connection between duality gaps in the original primal-dual pair and lack of strict complementarity in their homogeneous counterpart. Our emphasis is on results that deal with Semidefinite Programming, SDP. Copyright Springer Science+Business Media, LLC 2012

Keywords: Cone optimization; Duality; Preprocessing; Constraint qualification; Duality gap; Semidefinite programming; Strict complementarity; Nice cones; Devious cones; Facially dual complete cones (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10589-012-9480-0 (text/html)
Access to full text is restricted to subscribers.

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:53:y:2012:i:2:p:619-648

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

DOI: 10.1007/s10589-012-9480-0

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 ().