- A Complementarity Partition Theorem for Multifold Conic Systems Javier Peña (jfpandrew.cmu.edu) Vera Roshchina (vera.roshchinagmail.com) Abstract: Consider a homogeneous multifold convex conic system $$Ax = 0, \; x\in K_1\times \cdots \times K_r$$ and its alternative system $$A\transp y \in K_1^*\times \cdots \times K_r^*,$$ where $K_1,\dots, K_r$ are regular closed convex cones. We show that there is canonical partition of the index set $\{1,\dots,r\}$ 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. Keywords: Goldman-Tucker Theorem, complementarity in convex programming Category 1: Convex and Nonsmooth Optimization (Convex Optimization ) Category 2: Linear, Cone and Semidefinite Programming (Second-Order Cone Programming ) Citation: Download: [PDF]Entry Submitted: 08/03/2011Entry Accepted: 08/03/2011Entry Last Modified: 08/26/2011Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.