PENNON: A generalized augmented Lagrangian method for semidefinite programming. (English) Zbl 1044.90082
Di Pillo, Gianni (ed.) et al., High performance algorithms and software for nonlinear optimization. Selected lectures presented at the workshop, Erice, Italy, June 30 –July 8, 2001. Boston, MA: Kluwer Academic Publishers (ISBN 1-4020-7532-4/hbk). Appl. Optim. 82, 303-321 (2003).
Summary: This article describes a generalization of the PBM method by Ben-Tal and Zibulevsky to convex semidefinite programming problems. The algorithm used is a generalized version of the augmented Lagrangian method. We present details of this algorithm as implemented in a new code PENNON. The code can also solve second-order conic programming (SOCP) problems, as well as problems with a mixture of SDP, SOCP and NLP constraints. Results of extensive numerical tests and comparison with other SDP codes are presented.