A unifying framework for several cutting plane algorithms for semidefinite programming

Kartik Krishnan (kartikcaam.rice.edu)
John E. Mitchell (mitchjrpi.edu)

Abstract: Cutting plane methods provide the means to solve large scale semidefinite programs (SDP) cheaply and quickly. They can also conceivably be employed for the purposes of re-optimization after branching, or the addition of cutting planes. We give a survey of various cutting plane approaches for SDP in this paper. These cutting plane approaches arise from various perspectives, and include techniques based on interior point cutting plane approaches, non-differentiable optimization, and finally an approach which mimics the simplex method for linear programming (LP). We present an accessible introduction to various cutting plane approaches that have appeared in the literature. We place these methods in a unifying framework which illustrates how each approach arises as a natural enhancement of a primordial LP cutting plane scheme based on a semi-infinite formulation of the SDP.

Keywords: Semidefinite programming, nondifferentiable optimization, interior point cutting plane methods, active set approaches

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

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 3: Infinite Dimensional Optimization (Semi-infinite Programming )

Citation: Technical Report, Department of Computing and Software, McMaster University, last revised September 2004. To appear in Optimization Methods and Software, 2005. Math Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180. http://www.rpi.edu/~mitchj/papers/opte.html

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Entry Submitted: 11/27/2002
Entry Accepted: 11/27/2002
Entry Last Modified: 03/09/2005

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