Projection methods for conic feasibility problems: applications to polynomial sum-of-squares decompositions

Authors:
Didier Henrion;Jerome Malick
Affiliations:
LAAS, CNRS, University of Toulouse, Toulouse, France,Faculty of Electrical Engineering, Czech Technical University in Prague, Prague, Czech Republic;CNRS, Laboratoire Jean Kuntzmann, University of Grenoble, Grenoble, France
Venue:
Optimization Methods & Software
Year:
2011

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Abstract

This paper presents a projection-based approach for solving conic feasibility problems. To find a point in the intersection of a cone and an affine subspace, we simply project a point onto this intersection. This projection is computed by dual algorithms operating a sequence of projections onto the cone and generalizing the alternating projection method. We release an easy-to-use Matlab package implementing an elementary dual-projection algorithm. Numerical experiments show that, for solving some semidefinite feasibility problems, the package is competitive with sophisticated conic programming software. We also provide a particular treatment for semidefinite feasibility problems modelling polynomial sum-of-squares decomposition problems.