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Solving large scale problems over the doubly nonnegative cone

Thomas Davi (davi***at***opt.uni-duesseldorf.de)
Florian Jarre (jarre***at***opt.uni-duesseldorf.de)

Abstract: The recent approach of solving large scale semidefinite programs with a first order method by minimizing an augmented primal-dual function is extended to doubly nonnegative programs. Regularity of the augmented primal-dual function is established under the condition of uniqueness and strict complementarity. The application to the doubly nonnegative cone is motivated by the fact that the cost per iteration does not increase by adding nonnegativity constraints. Numerical experiments indicate that this extension is a particularly rewarding application.

Keywords: Semidefinite program, doubly nonnegative cone, regularity, augmented primal-dual function, orthogonal projection.

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Citation: The final publication is available at http://link.springer.com DOI: 10.1007/s10107-013-0687-3

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Entry Submitted: 04/20/2011
Entry Accepted: 04/20/2011
Entry Last Modified: 06/21/2013

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