A smoothing Newton method for the second-order cone complementarity problem

J. Burke, S. Xu: A non-interior predictor-corrector path-following algorithm for LCP. Reformulation: Nonsmooth, Piecewise Smooth and Smoothing Methods (M. Fukushima, L. Qi, eds.). Kluwer Academic Publishers, Boston, 1999, pp. 45–63.

J. Burke, S. Xu: A non-interior predictor-corrector path following algorithm for the monotone linear complementarity problem. Math. Program. 87 (2000), 113–130.

B. Chen, X. Chen: A global and local superlinear continuation-smoothing method for P 0 + R 0 and monotone NCP. SIAM J. Optim. 9 (1999), 624–645.

B. Chen, X. Chen: A global linear and local quadratic continuation smoothing method for variational inequalities with box constraints. Comput. Optim. Appl. 17 (2000), 131–158.

B. Chen, N. Xiu: A global linear and local quadratic noninterior continuation method for nonlinear complementarity problems based on Chen-Mangasarian smoothing functions. SIAM J. Optim. 9 (1999), 605–623.

J. Chen: A new merit function and its related properties for the second-order cone complementarity problem. Pac. J. Optim. 2 (2006), 167–179.

J. Chen, X. Chen, P. Tseng: Analysis of nonsmooth vector-valued functions associated with second-order cones. Math. Program. 101 (2004), 95–117.

J. Chen, P. Tseng: An unconstrained smooth minimization reformulation of the second-order cone complementarity problem. Math. Program. 104 (2005), 293–327.

X. D. Chen, D. Sun, J. Sun: Complementarity functions and numerical experiments on some smoothing Newton methods for second-order-cone complementarity problems. Comput. Optim. Appl. 25 (2003), 39–56.

X. N. Chi, S. Y. Liu: Analysis of a non-interior continuation method for second-order cone programming. J. Appl. Math. Comput. 27 (2008), 47–61.

X. N. Chi, S. Y. Liu: A one-step smoothing Newton method for second-order cone programming. J. Comput. Appl. Math. 223 (2009), 114–123.

X. N. Chi, S. Y. Liu: A non-interior continuation method for second-order cone programming. Optimization 58 (2009), 965–979.

F. H. Clarke: Optimization and Nonsmooth Analysis. John Wiley & Sons, New York, 1983, reprinted by SIAM, Philadelphia, 1990.

L. Fang: A new one-step smoothing Newton method for nonlinear complementarity problem with P 0-function. Appl. Math. Comput. 216 (2010), 1087–1095.

L. Fang, G. P. He, Y. H. Hu: A new smoothing Newton-type method for second-order cone programming problems. Appl. Math. Comput. 215 (2009), 1020–1029.

M. Fukushima, Z. Luo, P. Tseng: Smoothing functions for second-order-cone complementarity problems. SIAM J. Optim. 12 (2002), 436–460.

S. Hayashi, N. Yamashita, M. Fukushima: A combined smoothing and regularized method for monotone second-order cone complementarity problems. SIAM J. Optimization 15 (2005), 593–615.

Z. H. Huang, J. Y. Han, D. C. Xu, L. P. Zhang: The non-interior continuation methods for solving the P0 function nonlinear complementarity problem. Sci. China, Ser. A 44 (2001), 1107–1114.

Z. H. Huang, T. Ni: Smoothing algorithms for complementarity problems over symmetric cones. Comput. Optim. Appl. 45 (2010), 557–579.

C. Ma, X. Chen: The convergence of a one-step smoothing Newton method for P0-NCP based on a new smoothing NCP-function. J. Comput. Appl. Math. 216 (2008), 1–13.

R. Mifflin: Semismooth and semiconvex functions in constrained optimization. SIAM J. Control. Optim. 15 (1977), 957–972.

S. H. Pan, J. S. Chen: A damped Gauss-Newton method for the second-order cone complementarity problem. Appl. Math. Optim. 59 (2009), 293–318.

S. H. Pan, J. S. Chen: A linearly convergent derivative-free descent method for the second-order cone complementarity problem. Optimization 59 (2010), 1173–1197.

L. Qi: Convergence analysis of some algorithms for solving nonsmooth equations. Math. Oper. Res. 18 (1993), 227–244.

L. Qi, J. Sun: A nonsmooth version of Newton’s method. Math. Program. 58 (1993), 353–367.

L. Qi, D. Sun: Improving the convergence of non-interior point algorithm for nonlinear complementarity problems. Math. Comput. 69 (2000), 283–304.

L. Qi, D. Sun, G. Zhou: A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities. Math. Program. 87 (2000), 1–35.

J. Y. Tang, G. P. He, L. Dong, L. Fang: A smoothing Newton method for second-order cone optimization based on a new smoothing function. Appl. Math. Comput. 218 (2011), 1317–1329.

K. C. Toh, R. H. Tütüncü, M. J. Todd: SDPT3 Version 3. 02-A MATLAB software for semidefinite-quadratic-linear programming, 2000. http://www.math.nus.edu.sg/~mattohkc/sdpt3.html .

A. Yoshise: Interior point trajectories and a homogeneous model for nonlinear complementarity problems over symmetric cones. SIAM J. Optim. 17 (2006), 1129–1153.

L. Zhang, J. Han, Z. Huang: Superlinear/quadratic one-step smoothing Newton method for P 0-NCP. Acta Math. Sin. 21 (2005), 117–128.

J. Zhang, K. Zhang: A variant smoothing Newton method for P 0-NCP based on a new smoothing function. J. Comput. Appl. Math. 225 (2009), 1–8.

G. Zhou, D. Sun, L. Qi: Numerical experiments for a class of squared smoothing Newton methods for box constrained variational inequality problems. Reformulation-Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods (M. Fukushima, L. Qi, eds.). Kluwer Academic Publishers, Boston, 1999, pp. 421–441.