## A Globally Convergent Successive Approximation Method for Severely Nonsmooth Equations (1995)

Venue: | SIAM J. Control Optim |

Citations: | 40 - 21 self |

### BibTeX

@ARTICLE{Qi95aglobally,

author = {Liqun Qi and Xiaojun Chen},

title = {A Globally Convergent Successive Approximation Method for Severely Nonsmooth Equations},

journal = {SIAM J. Control Optim},

year = {1995},

volume = {33},

pages = {402--418}

}

### OpenURL

### Abstract

. This paper presents a globally convergent successive approximation method for solving F (x) = 0 where F is a continuous function. At each step of the method, F is approximated by a smooth function f k ; with k f k \Gamma F k! 0 as k ! 1. The direction \Gammaf 0 k (x k ) \Gamma1 F (x k ) is then used in a line search on a sum of squares objective. The approximate function f k can be constructed for nonsmooth equations arising from variational inequalities, maximal monotone operator problems, nonlinear complementarity problems and nonsmooth partial differential equations. Numerical examples are given to illustrate the method. Key words: Global convergence, successive approximation, integration convolution. AMS(MOS) subject classification. 90C30, 90C33 1. Introduction Let F : R n ! R n be a continuous, but not necessarily differentiable, function. We consider the system of nonlinear equations F (x) = 0; x 2 R n : (1) The recent literature of such nonsmooth equations inc...