-

 

 

 




Optimization Online





 

A Complementarity Partition Theorem for Multifold Conic Systems

Javier Peņa (jfp***at***andrew.cmu.edu)
Vera Roshchina (vera.roshchina***at***gmail.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: 08/03/2011
Entry Accepted: 08/03/2011
Entry Last Modified: 08/26/2011

Modify/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
Mathematical Optimization Society