A unifying framework for several cutting plane methods for semidefinite programming

Download the paper, pdf.


Kartik Krishnan
Department of Computing & Software
McMaster University
Hamilton, ON L8S 4K1
kksivara at ncsu.edu

John E. Mitchell
Department of Mathematical Sciences
Rensselaer Polytechnic Institute
Troy, NY 12180 USA

Optimization Methods and Software, 21(1), February 2006, pages 57-74.


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.

Download the paper, pdf.

Optimization Online listing

Return to my list of papers.