A new non-monotone SQP algorithm for the minimax problem

Abstract

In this paper, a new sequential quadratic programming (SQP) algorithm is proposed to solve the minimax problem which uses the idea of nonmonotonicity. The problem is transformed into an equivalent inequality constrained nonlinear optimization problem. In order to prevent the scaling problem, we do some modifications to the minimization problem. By the non-monotone SQP method, the new algorithm is globally convergent without using a penalty function. Furthermore, it is shown that the proposed method does not suffer from the Maratos effect, so the locally superlinear convergence is achieved. Numerical results suggest that our algorithm for solving the minmax problem is efficient and robust.

Keywords:

• minimax problem
• constrained optimization
• nonmonotonicity
• SQP
• convergence

AMS subject Classification :

• 65K05
• 90C30

Acknowledgements

We are grateful to the Editor and anonymous referees for your useful and detailed comments. This research is supported by the National Science Foundation of China (No. 10571137 and No. 10771162) and the Shanghai Excellent Young Teacher Foundation.