### A MULTIDIMENSIONAL FILTER SQP ALGORITHM FOR NONLINEAR PROGRAMMING

Wenjuan Xue, Weiai Liu

1. 1. School of Mathematics and Physics, Shanghai University of Electric Power, Shanghai 200090, China;
2. Department of Mathematics and Physics, Shanghai Dianji University, Shanghai 200240, China
• Received:2018-03-27 Revised:2018-12-27 Online:2020-09-15 Published:2021-03-11
• Supported by:
The authors would like to thank the Associate Editor and anonymous referees for their helpful suggestions. This work is supported by National Science Foundation of China (No.11601318) and Equipment Manufacturing Systems and Optimization (No. 13XKJC01).

Wenjuan Xue, Weiai Liu. A MULTIDIMENSIONAL FILTER SQP ALGORITHM FOR NONLINEAR PROGRAMMING[J]. Journal of Computational Mathematics, 2020, 38(5): 683-704.

We propose a multidimensional filter SQP algorithm. The multidimensional filter technique proposed by Gould et al.[SIAM J. Optim., 2005] is extended to solve constrained optimization problems. In our proposed algorithm, the constraints are partitioned into several parts, and the entry of our filter consists of these different parts. Not only the criteria for accepting a trial step would be relaxed, but the individual behavior of each part of constraints is considered. One feature is that the undesirable link between the objective function and the constraint violation in the filter acceptance criteria disappears. The other is that feasibility restoration phases are unnecessary because a consistent quadratic programming subproblem is used. We prove that our algorithm is globally convergent to KKT points under the constant positive generators (CPG) condition which is weaker than the well-known Mangasarian-Fromovitz constraint qualification (MFCQ) and the constant positive linear dependence (CPLD). Numerical results are presented to show the efficiency of the algorithm.

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