EconPapers    
Economics at your fingertips  
 

A Conic Duality Frank--Wolfe-Type Theorem via Exact Penalization in Quadratic Optimization

Werner Schachinger () and Immanuel Bomze
Additional contact information
Werner Schachinger: Department of Statistics and Decision Support Systems, University of Vienna, A-1210 Vienna, Austria

Mathematics of Operations Research, 2009, vol. 34, issue 1, 83-91

Abstract: The famous Frank--Wolfe theorem ensures attainability of the optimal value for quadratic objective functions over a (possibly unbounded) polyhedron if the feasible values are bounded. This theorem does not hold in general for conic programs where linear constraints are replaced by more general convex constraints like positive semidefiniteness or copositivity conditions, despite the fact that the objective can be even linear. This paper studies exact penalizations of (classical) quadratic programs, i.e., optimization of quadratic functions over a polyhedron, and applies the results to establish a Frank--Wolfe-type theorem for the primal-dual pair of a class of conic programs that frequently arises in applications. One result is that uniqueness of the solution of the primal ensures dual attainability, i.e., existence of the solution of the dual.

Keywords: copositive programming; dual attainability (search for similar items in EconPapers)
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed

Downloads: (external link)
http://dx.doi.org/10.1287/moor.1080.0345 (application/pdf)

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:inm:ormoor:v:34:y:2009:i:1:p:83-91

Access Statistics for this article

More articles in Mathematics of Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Matthew Walls ().

 
Page updated 2020-07-24
Handle: RePEc:inm:ormoor:v:34:y:2009:i:1:p:83-91