Dual Newton’s Methods for Linear Second-Order Cone Programming
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The linear second-order cone programming problem is considered. For its solution, two dual Newton’s methods are proposed. These methods are constructed with the help of optimality conditions. The nonlinear system of equations, obtained from the optimality conditions and depended only from dual variables, is solved by the Newton method. Under the assumption that there exist strictly complementary solutions of both primal and dual problems the local convergence of the methods with super-linear rate is proved.
KeywordsLinear second-order cone programming Dual Newton’s method Local convergence Super-linear rate of convergence