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Javier Peņa (jfpandrew.cmu.edu) 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 GoldmanTucker Theorem for linear programming. Keywords: GoldmanTucker Theorem, complementarity in convex programming Category 1: Convex and Nonsmooth Optimization (Convex Optimization ) Category 2: Linear, Cone and Semidefinite Programming (SecondOrder Cone Programming ) Citation: Download: [PDF] Entry Submitted: 08/03/2011 Modify/Update this entry  
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