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Copositive optimization - recent developments and applications

Immanuel M. Bomze(immanuel.bomze***at***univie.ac.at)

Abstract: Due to its versatility, copositive optimization receives increasing interest in the Operational Research community, and is a rapidly expanding and fertile field of research. It is a special case of conic optimization, which consists of minimizing a linear function over a cone subject to linear constraints. The diversity of copositive formulations in different domains of optimization is impressive, since problem classes both in the continuous and discrete world, as well as both deterministic and stochastic models are covered. Copositivity appears in local and global optimality conditions for quadratic optimization, but can also yield tighter bounds for NP-hard combinatorial optimization problems. Here some of the recent success stories are told, along with principles, algorithms and pplications.

Keywords: approximation hierarchy; clique number; completely positive matrix; convexity gap; crossing number; Lyapunov function; robust optimization; standard quadratic optimization; strict complementarity

Category 1: Linear, Cone and Semidefinite Programming (Other )

Category 2: Nonlinear Optimization (Quadratic Programming )

Category 3: Integer Programming ((Mixed) Integer Nonlinear Programming )

Citation: To appear in: European J. Operational Research (invited review)

Download: [PDF]

Entry Submitted: 06/07/2011
Entry Accepted: 06/07/2011
Entry Last Modified: 06/07/2011

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