A Trust Region Algorithm with Memory for Equality Constrained Optimization

Abstract

In this paper, we present a trust region algorithm with memory for equality constrained optimization problems. Different from the traditional trust region algorithms, our trust region model includes memory of the past iterations, which makes the algorithm more farsighted in the sense that its behavior is not completely dominated by the local nature of the objective function, but rather by a more global view. The global convergence is established by using a nonmonotone technique. We report numerical tests to examine the effectiveness of the algorithm.

Keywords:

• Global convergence
• Memory model
• Nonmonotone technique
• Trust region algorithm

AMS Subject Classification:

• 65K05
• 90C30

ACKNOWLEDGMENTS

The authors would like to express their sincere gratitude to the editor and referees for their helpful comments and suggestions.

This work is supported by the National Natural Science Foundation of China (No. 10671126 and 10571106) and Shanghai Leading Academic Discipline Project (T0502).