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Published in:
2020 | OriginalPaper | Chapter
Dual Newton’s Methods for Linear Second-Order Cone Programming
Author : Vitaly Zhadan
Published in: Mathematical Optimization Theory and Operations Research
Publisher: Springer International Publishing
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Abstract
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.