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A new one-step smoothing Newton method for second-order cone programming. (English) Zbl 1265.90229
The paper deals with the second-order cone programming (SOCP) problem. The authors present a one-step smoothing Newton method for solving the SOCP problem based on a new smoothing function of the Fischer-Burmeister function. The algorithm solves only one system of linear equations and performs only one Armijo-type line-search per iteration. Global and local quadratic convergence under standard assumptions are proved. Numerical experiments demonstrate efficiency of the algorithm.

90C25 Convex programming
90C46 Optimality conditions and duality in mathematical programming
65K05 Numerical mathematical programming methods
49M15 Newton-type methods
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