Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2003-011 (August 29, 2003)

Successive linearization methods for nonlinear semidefinite programs
by Christian Kanzow, Christian Nagel and Masao Fukushima

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We present a successive linearization method with a trust region-type globalization for the solution of nonlinear semidefinite programs. At each iteration, the method solves a quadratic semidefinite program, which can be converted to a linear semidefinite program with a second order cone constraint. A subproblem of this kind can be solved quite efficiently by using some recent software for semidefinite and second-order cone programs. The method is shown to be globally convergent under certain assumptions. Some numerical results are included in order to illustrate its behavior.