An infeasible QP-free algorithm without a penalty function or a filter for nonlinear inequality-constrained optimization

Abstract

In this paper, we present an infeasible quadratic programming-free method without using a penalty function or a filter for inequality-constrained optimization. At each iteration, three linear equations with the same coefficient matrix are solved. Furthermore, the nearly active set technique is used to reduce the amount of computational work. Under mild conditions, we prove that the proposed method has global and superlinear local convergence. At last, preliminary numerical results and comparison are reported.

Keywords:

• infeasible QP-free method
• penalty-function-free
• filter-free
• working set
• global convergence
• superlinear convergence

Acknowledgments

The authors wish to express their sincere thanks to the referees and editor for careful reading of the manuscript and their many comments and suggestions which greatly improved the presentation.

Funding

The National Science Foundation of China (No. 11371281, No. 11271259, No. 11271266), Innovation Program of Shanghai Municipal Education Commission (No. 12YZ172) and Equipment Manufacturing Systems and Optimization (No.13XKJC01).