Dual Newton's methods for linear second-order cone programming (Q2663719)

In this paper, authors have contemplated linear second-order cone programming problem. The second-order cone programming problem is an important problem in cone programming to study. Two different variations of the dual Newton's method for solving linear second order cone programming problem is presented in this paper. These methodologies are formulated with the help of optimality conditions. The nonlinear system of equations which are procured from the optimality conditions and determined wholly from dual variables are solved by the Newton method. The authors proved the local convergence of the methods with super-linear rate with the presumption that strictly complementary solutions exists for both primal and dual problems. From theoretical point of view, when the number of equalities in the primal problem is not large, dual methods are preferred more in comparison to the primal methods. Moreover, in the case of non-degenerate problems, these dual methods are well posed. Theorems and results are explained and well proved in the paper exhibiting the solution approach for second-order cone programming problem. For the entire collection see [Zbl 1458.90004].