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最优化对数障碍法
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Abstract:
在求解不等式约束优化问题中对数障碍函数方法是非常流行的,众所周知,对数障碍函数在线性规划与线性半定规划的内点方法中起着重要的作用。本文主要介绍了对数障碍方法及其算法,并通过计算例子说明此方法的有效性。
The method of solving the logarithmic barrier function method is very popular in solving the non-equality constraint optimization problem, it is well known that the logarithmic barrier function plays an important role in linear planning and linear semi-planning. This paper mainly introduces the logarithmic barrier method and its algorithm, and the effectiveness of this method is illustrated by calculating examples.
[1] | 袁亚湘, 孙文瑜. 最优化理论与方法[M]. 北京: 科学出版社, 1997. |
[2] | Polak, E., Higgins, J.E. and Mayne, D.Q. (1992) A Barrier Function Method for Minimax Problems. Mathematical Programming, 54, 155-176. https://doi.org/10.1007/BF01586049 |
[3] | Pourmohamad, T. and Lee, H.K.H. (2022) Bayesian Optimization via Barrier Functions. Jour- nal of Computational and Graphical Statistics, 31, 74-83. https://doi.org/10.1080/10618600.2021.1935270 |
[4] | Zhang, R., Mei, J., Dai, B., Schuurmans, D. and Li, N. (2022) On the Effect of Log-Barrier Regularization in Decentralized Softmax Gradient Play in Multiagent Systems. arXiv preprint arXiv:2202.00872 |
[5] | 陈宝林. 最优化理论与算法[M]. 北京: 清华大学出版社有限公司, 2005. |
[6] | Frisch, K.R. (1955) The Logarithmic Potential Method of Convex Programming. Memoran- dum, University Institute of Economics, Oslo, 5. |
[7] | Wright, M.H. (1992) Interior Methods for Constrained Optimization. Acta Numerica, 1, 341-407. https://doi.org/10.1017/S0962492900002300 |
[8] | Fiacco, A.V. and McCormick, G.P. (1990) Nonlinear Programming: Sequential Unconstrained Minimization Techniques. Society for Industrial and Applied Mathematics, Philadelphia, PA. https://doi.org/10.1137/1.9781611971316 |
[9] | Fang, S.-C. and Puthenpura, S. (1993) Linear Optimization and Extensions: Theory and Algorithms. Prentice-Hall, Inc., Hoboken. |