# American Institute of Mathematical Sciences

April  2005, 1(2): 235-250. doi: 10.3934/jimo.2005.1.235

## A smoothing projected Newton-type method for semismooth equations with bound constraints

 1 Institute of Mathematics, Changsha University of Science and Technology, Changsha, China 2 Institute of Applied Mathematics, Hunan University, Changsha, China

Received  June 2004 Revised  December 2005 Published  April 2005

This paper develops a smoothing algorithm to solve a system of constrained equations. Compared with the traditional methods, the new method does not need the continuous differentiability assumption for the corresponding merit function. By using some perturbing technique and suitable strategy of the chosen search direction, we find that the new method not only keeps the strict positivity of the smoothing variable at any non-stationary point of the corresponding optimization problem, but also enjoys global convergence and locally superliner convergence. The former character is the key requirement for smoothing methods. Some numerical examples arising from semi-infinite programming (SIP) show that the new algorithm is promising.
Citation: Xiaojiao Tong, Shuzi Zhou. A smoothing projected Newton-type method for semismooth equations with bound constraints. Journal of Industrial & Management Optimization, 2005, 1 (2) : 235-250. doi: 10.3934/jimo.2005.1.235
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