A classical method for solving the variational inequality problem is the projection algorithm. We show that existing convergence results for this algorithm follow from one given by Gabay for a splitting algorithm for finding a zero of the sum of two maximal monotone operators. Moreover, we extend the projection algorithm to solve any monotone affine variational inequality problem. When applied ...

A variational inequality problem (VIP) satisfying a constraint qual-iication can be reduced to a mixed complementarity problem (MCP). Monotonicity of the VIP implies that the MCP is also monotone. Introducing regularizing perturbations, a sequence of strictly monotone mixed complementarity problems is generated. It is shown that, if the original problem is solvable, the sequence of computable i...

This paper extends the derivative-free descent method [18] for the nonlinear complementarity problem to the symmetric cone complementarity problem (SCCP). The algorithm is based on the unconstrained implicit Lagrangian reformulation of the SCCP, but uses a convex combination of the negative partial gradients of the implicit Lagrangian function ψα, i.e. the vector of the form −θ∇xψα −(1 −θ)∇yψα ...

We consider the linear monotone complementarity problem for domains obtained as the intersection of an aane subspace and the Cartesian product of symmetric cones. A primal-dual potential reduction algorithm is described and its complexity estimates are established with the help of the Jordan-algebraic technique .

An interior point method for monotone linear complementarity problems acting in a wide neighborhood of the central path is presented. The method has O( √ nL)iteration complexity and is superlinearly convergent even when the problem does not possess a strictly complementary solution.

we present an improved version of a full nesterov-todd step infeasible interior-point method for linear complementarityproblem over symmetric cone (bull. iranian math. soc.,40(3), 541-564, (2014)). in the earlier version, each iteration consistedof one so-called feasibility step and a few -at most three -centering steps. here, each iteration consists of only a feasibilitystep. thus, the new alg...

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 feasibility steps, finds...

This paper introduces the notion of a weighted Complementarity Problem (wCP), which consists in finding a pair of vectors (x, s) belonging to the intersection of a manifold with a cone, such that their product in a certain algebra, x ◦ s, equals a given weight vector w. When w is the zero vector, then wCP reduces to a Complementarity Problem (CP). The motivation for introducing the more general...

The literature on interior point algorithms shows impressive results related to the speed of convergence of the objective values, but very little is known about the convergence of the iterate sequences. This paper studies the horizontal linear complementarity problem, and derives general convergence properties for algorithms based on Newton iterations. This problem provides a simple and general...