Numerical Algebra, Control and Optimization (NACO)

On methods for solving nonlinear semidefinite optimization problems

Pages: 1 - 14, Volume 1, Issue 1, March 2011      doi:10.3934/naco.2011.1.1

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Jie Sun - School of Business, National University of Singapore, 119245, Singapore (email)

Abstract: The nonlinear semidefinite optimization problem arises from applications in system control, structural design, financial management, and other fields. However, much work is yet to be done to effectively solve this problem. We introduce some new theoretical and algorithmic development in this field. In particular, we discuss first and second-order algorithms that appear to be promising, which include the alternating direction method, the augmented Lagrangian method, and the smoothing Newton method. Convergence theorems are presented and preliminary numerical results are reported.

Keywords:  Alternating direction method, augmented Lagrangian method, semismooth Newton method.
Mathematics Subject Classification:  Primary: 90C22; Secondary: 90C25.

Received: November 2010;      Revised: November 2010;      Available Online: February 2011.