Combining Trust Region and Line Search Methods for Equality Constrained Optimization

Abstract

In this article, we combine trust region techniques and line search techniques to develop an iterative method for nonlinear equality constrained optimization. At each iteration, a trust region subproblem is solved. By using a suitable updated approach of penalty parameter, we prove that the solution of the subproblem provides a descent direction for the chosen merit function. Then if the solution of the subproblem of the trust region method is rejected, we use a line search method to obtain the next iterative point. Compared with traditional trust region methods, the new algorithm never resolves the trust region subproblem and is more economical. Hence, the new algorithm proposed in this article shares advantages of trust region methods and line search methods. Under some ordinary conditions, the global convergence of the new algorithm is proved. Numerical results are also presented.

Keywords:

• Line search method
• Trust region method
• Combining technique
• Equality constrained optimization
• Global convergence
• AMS Subject Classifications: 65K05
• 49D37

Acknowledgment

The authors would like to thank the referee and Professor Xiaojun Chen for their helpful comments.