A variational method for unconstrained optimization problems

Abstract

We introduce a new method for solving an unconstrained optimization problem. The method is based on the solution of a variational inequality problem and may be considered a modified trust region algorithm. We prove the convergence of the method and present some numerical results.

Keywords:

• Trust region method
• Unconstrained optimization
• Variational inequality

Acknowledgements

The author wishes to thank the referees and editor for their helpful comments on an earlier version of this paper.