Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2006-005 (April 20, 2006)

Semismooth Methods for Linear and Nonlinear Second-Order Cone Programs
by Christian Kanzow and Masao Fukushima

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The optimality conditions of a nonlinear second-order cone program can be reformulated as a nonsmooth system of equations using a projection mapping. This allows the application of nonsmooth Newton methods for the solution of the nonlinear second-order cone program. Conditions for the local quadratic convergence of these nonsmooth Newton methods are investigated. Related conditions are also given for the special case of a linear second-order cone program. An interesting and important feature of these conditions is that they do not require strict complementarity of the solution.