Optimization Online


Homogeneous Cone Complementarity Problems and $P$ Properties

Lingchen Kong (konglchen***at***126.com)
Levent Tuncel (ltuncel***at***math.uwaterloo.ca)
Naihua Xiu (nhxiu***at***center.njtu.edu.cn)

Abstract: We consider existence and uniqueness properties of a solution to homogeneous cone complementarity problem (HCCP). Employing the $T$-algebraic characterization of homogeneous cones, we generalize the $P, P_0, R_0$ properties for a nonlinear function associated with the standard nonlinear complementarity problem to the setting of HCCP. We prove that if a continuous function has either the order-$P_0$ and $R_0$, or the $P_0$ and $R_0$ properties then all the associated HCCPs have solutions. In particular, if a continuous function has the trace-$P$ property then the associated HCCP has a unique solution (if any); if it has the uniform-trace-$P$ property then the associated HCCP has the global uniqueness (of the solution) property (GUS). We present a necessary condition for a nonlinear transformation to have the GUS property. Moreover, we establish a global error bound for the HCCP with the uniform-trace-$P$ property. Finally, we study the HCCP with the relaxation transformation on a $T$-algebra and automorphism invariant properties for homogeneous cone linear complementarity problem.

Keywords: Homogeneous cone complementarity problem, $P$ property, existence of a solution, globally uniquely solvability property, error bound

Category 1: Complementarity and Variational Inequalities

Citation: Research Report, April 2009.

Download: [PDF]

Entry Submitted: 04/13/2009
Entry Accepted: 04/16/2009
Entry Last Modified: 11/11/2010

Modify/Update this entry

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


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Programming Society