On methods for solving nonlinear semidefinite optimization problems

Jie Sun

doi:10.3934/naco.2011.1.1

Article Contents

2011, Volume 1, Issue 1: 1-14. Doi: 10.3934/naco.2011.1.1

This issue Previous Article Preface Next Article Recent advances in numerical methods for nonlinear equations and nonlinear least squares

On methods for solving nonlinear semidefinite optimization problems

Jie Sun^1,

1.
School of Business, National University of Singapore, 119245

Received: November 2010

Revised: November 2010

Published: February 2011

Abstract / Introduction Related Papers Cited by

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:

Mathematics Subject Classification: Primary: 90C22; Secondary: 90C25.

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