Homogeneous Cone Complementarity Problems and $P$ Properties

Details Homogeneous Cone Complementarity Problems and $P$ Properties Homogeneous Cone Complementarity Problems and $P$ Properties

2009-04-11

arxiv.org/abs/0904.1827v2

Mathematics

Optimization and Control

18 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Homogeneous Cone Complementarity Problems and $P$ Properties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Homogeneous Cone Complementarity Problems and $P$ Properties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Homogeneous Cone Complementarity Problems and $P$ Properties will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-239885