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A new one‐step smoothing newton method for the second‐order cone complementarity problem
Author(s) -
Fang Liang,
Han Congying
Publication year - 2011
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1366
Subject(s) - mathematics , smoothing , parameterized complexity , line search , newton's method , complementarity theory , complementarity (molecular biology) , mixed complementarity problem , quadratic equation , mathematical optimization , nonlinear complementarity problem , convergence (economics) , algorithm , nonlinear system , computer science , geometry , statistics , physics , computer security , biology , quantum mechanics , economics , radius , genetics , economic growth
In this paper, we present a new one‐step smoothing Newton method for solving the second‐order cone complementarity problem (SOCCP). Based on a new smoothing function, the SOCCP is approximated by a family of parameterized smooth equations. At each iteration, the proposed algorithm only need to solve one system of linear equations and perform only one Armijo‐type line search. The algorithm is proved to be convergent globally and superlinearly without requiring strict complementarity at the SOCCP solution. Moreover, the algorithm has locally quadratic convergence under mild conditions. Numerical experiments demonstrate the feasibility and efficiency of the new algorithm. Copyright © 2010 John Wiley & Sons, Ltd.