A method for non-differentiable optimization problems

Abstract

We introduce a new method for solving a class of non-smooth unconstrained optimization problems. The method constructs a sequence<texlscub>x _k </texlscub>in ℝ ⁿ , and at the kth iteration, a search direction h _k is considered, where h _k is a solution to a variational inequality problem. A convergence theorem for our algorithm model and its discrete version can be easily proved. Furthermore, preliminary computational results show that the new method performs quite well and can compete with other methods.

Keywords:

• variational inequality
• unconstrained optimization
• non-differentiable problems

2000 AMS Subject Classifications :

• 65K05
• 65K10
• 93E25