-

 

 

 




Optimization Online





 

Weighted LCPs and interior point systems for copositive linear transformations on Euclidean Jordan algebras

M. S. Gowda(gowda***at***umbc.edu)

Abstract: In the setting of a Euclidean Jordan algebra V with symmetric cone V_+, corresponding to a linear transformation M, a `weight vector' w in V_+, and a q in V, we consider the weighted linear complementarity problem wLCP(M,w,q) and (when w is in the interior of V_+) the interior point system IPS(M,w,q). When M is copositive and q satisfies an interiority condition, we show that both the problems have solutions. A simple consequence, stated in the setting of R^n is that when M is a copositive plus matrix and q is strictly feasible for the linear complementarity problem LCP(M,q), the corresponding interior point system has a solution. This is analogous to a well-known result of Kojima et al. on P_*-matrices and may lead to interior point methods for solving copositive LCPs.

Keywords: Weighted LCP, Interior point system, Euclidean Jordan algebra, Degree, Copositive linear transformation

Category 1: Complementarity and Variational Inequalities

Citation: Research Report, Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, Maryland 21250, USA, July 2018.

Download: [PDF]

Entry Submitted: 07/25/2018
Entry Accepted: 07/25/2018
Entry Last Modified: 07/25/2018

Modify/Update this entry


  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository

 

Submit
Update
Policies
Coordinator's Board
Classification Scheme
Credits
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society