Extended Lorentz cones and mixed complementarity problems

Abstract

In this paper we extend the notion of a Lorentz cone. We call a closed convex set isotone projection set with respect to a pointed closed convex cone if the projection onto the set is isotone (i.e., monotone) with respect to the order defined by the cone. We determine the isotone projection sets with respect to an extended Lorentz cone. In particular a Cartesian product between an Euclidean space and any closed convex set in another Euclidean space is such a set. We use this property to find solutions of general mixed complementarity problems in an iterative way.

15 pages

References in corpus (2)

• Self-dual cones, generalized lattice operations and isotone projections
• Lattice-like operations and isotone projection sets

Cited by in corpus (8)

• Complementarity and Related Problems
• Stochastic Linear Complementarity Problems on Extended Second Order Cones
• Positive operators of Extended Lorentz cones
• How to project onto extended second order cones
• Generalized power cones: optimal error bounds and automorphisms
• Extended Lorentz cones and variational inequalities on cylinders
• The monotone extended second order cone and mixed complementarity problems
• Linear complementarity problems on extended second order cones