A Complementarity Partition Theorem for Multifold Conic Systems
Year: 2011
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Peña, Javier, Roshchina, Vera
Institutions: Carnegie Mellon University, University of Évora
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2952412181