On methods for solving nonlinear semidefinite optimization problems
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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.
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Numerical Algebra, Control and Optimization following peer review. The definitive publisher-authenticated version Sun, J. 2011. On methods for solving nonlinear semidefinite optimization problems. Numerical Algebra, Control and Optimization. 1: pp. 1-14.is available online at: http://doi.org/10.3934/naco.2011.1.1
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