In this paper, efforts are made to solve nonlinear programming with many complicated constraints more efficiently. The constrained optimization problem is firstly converted to a minimax problem, where the max-value function is approximately smoothed by the so-called flattened aggregate function or its modified version. For carefully updated aggregate parameters, the smooth unconstrained optimization problem is solved by an inexact Newton method. Because the flattened aggregate function can usually reduce greatly the amount of computation for gradients and Hessians, the method is more efficient. Convergence of the proposed method is proven and some numerical results are given to show its efficiency.
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This work is financially supported by the Innovation Talent Training Program of Science and Technology of Jilin Province of China (20180519011JH), the Science and Technology Development Project Program of Jilin Province (20190303132SF), and the Project of Education Department of Jilin Province (JJKH20200028KJ).
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Jiang, X., Yang, Y., Lu, Y. et al. Flattened aggregate function method for nonlinear programming with many complicated constraints. Numer Algor 86, 103–122 (2021). https://doi.org/10.1007/s11075-020-00881-1
- Nonlinear programming
- Complicated constraints
- Minimax problem
- Flattened aggregate function
- Inexact Newton method
Mathematics Subject Classification (2010)