A Complementarity Partition Theorem for Multifold Conic Systems

Abstract

Consider a homogeneous multifold convex conic system $$Ax=0,x\in K_1\times ...\times K_r$$ and its alternative system $$ A\transp y \in K_1^*\times...\times K_r^*, $$ where $K_1,...,K_r$ are regular closed convex cones. We show that there is canonical partition of the index set $1,...,r$ determined by certain complementarity sets associated to the most interior solutions to the two systems. Our results are inspired by and extend the Goldman-Tucker Theorem for linear programming.

12 pages, 2 figures