An area-type nonmonotone filter method for nonlinear constrained optimization

Ke Su; Wei Lu; Shaohua Liu; Ke Su; Wei Lu; Shaohua Liu

doi:10.3934/math.20221120

AIMS Mathematics

2022, Volume 7, Issue 12: 20441-20460. doi: 10.3934/math.20221120

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Research article

An area-type nonmonotone filter method for nonlinear constrained optimization

1.
College of Mathematics and Information Science, Hebei University, Baoding, China
2.
Key Laboratory of Machine Learning and Computational Intelligence, Hebei University, Baoding, China

Received: 26 July 2022 Revised: 28 August 2022 Accepted: 08 September 2022 Published: 19 September 2022
MSC : 65K05, 90C30

In this paper, we define a new area-type filter algorithm based on the trust-region method. A relaxed trust-region quadratic correction subproblem is proposed to compute the trial direction at the current point. Consider the objective function and the constraint violation function at the current point as a point pair. We divide the point pairs into different partitions by the dominant region of the filter and calculate the contributions of the point pairs to the area of the filter separately. Different from the conventional filter, we define the contribution as the filter acceptance criterion for the trial point. The nonmonotone area-average form is also adopted in the filter mechanism. In this paper, monotone and nonmonotone methods are proposed and compared with the numerical values. Furthermore, the algorithm is proved to be convergent under some reasonable assumptions. The numerical experiment shows the effectiveness of the algorithm.
- area-type filter,
- trust-region,
- nonlinear programming,
- monotone,
- nonmonotone
Citation: Ke Su, Wei Lu, Shaohua Liu. An area-type nonmonotone filter method for nonlinear constrained optimization[J]. AIMS Mathematics, 2022, 7(12): 20441-20460. doi: 10.3934/math.20221120

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Abstract

In this paper, we define a new area-type filter algorithm based on the trust-region method. A relaxed trust-region quadratic correction subproblem is proposed to compute the trial direction at the current point. Consider the objective function and the constraint violation function at the current point as a point pair. We divide the point pairs into different partitions by the dominant region of the filter and calculate the contributions of the point pairs to the area of the filter separately. Different from the conventional filter, we define the contribution as the filter acceptance criterion for the trial point. The nonmonotone area-average form is also adopted in the filter mechanism. In this paper, monotone and nonmonotone methods are proposed and compared with the numerical values. Furthermore, the algorithm is proved to be convergent under some reasonable assumptions. The numerical experiment shows the effectiveness of the algorithm.

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