2009/04/11 by Lingchen Kong, Kong, Lingchen, Levent Tunçel +3
Computer Science · Mathematics · #26B05 #65K05 #90C33 #Advanced Optimization Algorithms Research #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #math.OC #msc:26B05 #msc:65K05 #msc:90C33
paper · pdf · doi:10.48550/arxiv.0904.1827
18 pages
openalex publication_date 2009/04/11 · arxiv created 2010/11/11 · arxiv updated 2010/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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, P0, R0 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-P0 and R0, or the P0 and R0 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.