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A damped Gauss-Newton method for the second-order cone complementarity problem. (English) Zbl 1169.49031
Summary: We investigate some properties related to the generalized Newton method for the Fischer-Burmeister (FB) function over second-order cones, which allows us to reformulate the second-order cone complementarity problem as a semismooth system of equations. Specifically, we characterize the B-subdifferential of the FB function at a general point and study the condition for every element of the B-subdifferential at a solution being nonsingular. In addition, for the induced FB merit function, we establish its coerciveness and provide a weaker condition than J.-S. Chen and P. Tseng [Math. Program. 104, No. 2–3 (B), 293–327 (2005; Zbl 1093.90063)] for each stationary point to be a solution, under suitable Cartesian P-properties of the involved mapping. By this, a damped Gauss-Newton method is proposed, and global and superlinear convergence results are obtained. Numerical results are reported for the second-order cone programs from the DIMACS library, which verify the good theoretical properties of the method.
49M15Newton-type methods in calculus of variations
49J52Nonsmooth analysis (other weak concepts of optimality)
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
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