Regularization Methods for Semidefinite Programming

Jérôme Malick, Janez Povh, Franz Rendl, Angelika Wiegele

Abstract: We introduce a new class of algorithms for solving linear semidefinite programming (SDP) problems. Our approach is based on classical tools from convex optimization such as quadratic regularization and augmented Lagrangian techniques. We study the theoretical properties and we show that practical implementations behave very well on some instances of SDP having a large number of constraints. We also show that the “boundary point method” from Povh, Rendl, and Wiegele [Computing, 78 (2006), pp. 277–286] is an instance of this class.