Open AccessA SMOOTHING NEWTON METHOD FOR NCP BASED ON A NEW CLASS OF SMOOTHING FUNCTIONS
Author(s) -
Jianguang Zhu,
Bin Hao
Publication year - 2014
Publication title -
journal of applied mathematics and computing. series a
Language(s) - English
Resource type - Journals
ISSN - 1598-5857
DOI - 10.14317/jami.2014.211
Subject(s) - smoothing , mathematics , class (philosophy) , mathematical optimization , function (biology) , complementarity (molecular biology) , newton's method , set (abstract data type) , algorithm , nonlinear system , computer science , artificial intelligence , statistics , genetics , physics , quantum mechanics , evolutionary biology , biology , programming language
A new class of smoothing functions is introduced in this paper, which includes some important smoothing complementarity functions as its special cases. Based on this new smoothing function, we proposed a smoothing Newton method. Our algorithm needs only to solve one linear system of equations. Without requiring the nonemptyness and boundedness of the solution set, the proposed algorithm is proved to be globally convergent. Numerical results indicate that the smoothing Newton method based on the new proposed class of smoothing functions with θ ∈ (0, 1) seems to have better numerical performance than those based on some other important smoothing functions, which also demonstrate that our algorithm is promising. AMS Mathematics Subject Classification : 65K05, 90C33.