We generalize the P, P0, R0 properties for a nonlinear function associated with the standard nonlinear complementarity problem to the setting of generalized nonlinear complementarity problem (GNCP). We prove that if a continuous function has the order P0 and R0 properties then all the associated GNCPs have solutions.

A new necessary and sufficient condition for the row W-property is given. By using this new condition and a special row rearrangement, we provide two global error bounds for the extended vertical linear complementarity problem under the row W-property, which extend the error bounds given in [2, 10] for the P-matrix linear complementarity problem, respectively. We show that one of the new error ...

For the extended linear complementarity problem 11], we introduce and characterize column-suuciency, row-suuciency, and P-properties. These properties are then specialized to the vertical , horizontal, and mixed linear complementarity problems.

In this paper we consider the extended semide nite linear complementarity problem (XSDLCP). We propose merit functions that can constitute minimization problems equivalent to XSDLCP and show some properties of these functions. We also consider the semide nite nonlinear complementarity problem (SDNCP) and give new su cient conditions that guarantee the existence of a solution to SDNCP.

In this paper, we study some basic properties of the monotone semide nite nonlinear complementarity problem (SDCP). We show that the trajectory continuously accumulates into the solution set of the SDCP passing through the set of the infeasible but positive de nite matrices under certain conditions. Especially, for the monotone semide nite linear complementarity problem, the trajectory converge...

‎a full nesterov-todd (nt) step infeasible interior-point algorithm‎ ‎is proposed for solving monotone linear complementarity problems‎ ‎over symmetric cones by using euclidean jordan algebra‎. ‎two types of‎ ‎full nt-steps are used‎, ‎feasibility steps and centering steps‎. ‎the‎ ‎algorithm starts from strictly feasible iterates of a perturbed‎ ‎problem‎, ‎and, using the central path and feasi...