Abstract
In this paper, we propose a line search penalty-free method for solving nonlinear second-order cone programming (NSOCP) problem. Compared with the traditional SQP-type method for NSOCP, our method does not need the assumption that the subproblem is feasible. Besides that, it does not use penalty-function or filter technique. We first use a robust linear second-order cone programming subproblem to get a detective step and then compute an optimal step from a quadratic optimization subproblem. The search direction is a convex combination of the detective step and optimal step. This two-phase strategy and the penalty-free technique are employed to promote global convergence which is analyzed under mild assumptions. We report some numerical experiments whose results show that the proposed algorithm is applicable and efficient.
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