Paper Info
Title
Simultaneous Diagonalization of Matrices and its Application in Quadratic Constrained Quadratic Programming
Abstract
An equivalence between attainability of simultaneous diagonalization (SD) and hidden convexity in quadratically constrained quadratic programming (QCQP) stimulates us to investigate necessary and sufficient SD conditions, which is one of the open problems posted by Hiriart-Urruty [SIAM Rev., 49 (2007), pp. 255-273] nine years ago. In this paper we give a necessary and sufficient SD condition for any two real symmetric matrices and offer a necessary and sufficient SD condition for any finite collection of real symmetric matrices under the existence assumption of a semidefinite matrix pencil. Moreover, we apply our SD conditions to QCQP, especially with one or two quadratic constraints, to verify the exactness of its second-order cone programming relaxation and to facilitate the solution process of QCQP.
Year
DOI
Venue
2016
10.1137/15M1023920
SIAM JOURNAL ON OPTIMIZATION
Keywords
Field
DocType
simultaneous diagonalization,congruence,quadratically constrained quadratic programming,second-order cone programming relaxation
Second-order cone programming,Mathematical optimization,Quadratic growth,Convexity,Quadratically constrained quadratic program,Matrix (mathematics),Quadratic equation,Symmetric matrix,Quadratic programming,Mathematics
Journal
Volume
Issue
ISSN
26
3
1052-6234
Citations 
PageRank 
References 
0
0.34
0
Authors
2
Name
Order
Citations
PageRank
rujun jiang100.34
Duan Li25612.31