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An Inexact Accelerated Proximal Gradient Method and a Dual Newton-CG Method for the Maximal Entropy Problem

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Abstract

This paper describes an algorithm to solve large-scale maximal entropy problems. The algorithm employs an inexact accelerated proximal gradient method to generate an initial iteration point which is important; then it applies the Newton-CG method to the dual problem. Numerical experiments illustrate that the algorithm can supply an acceptable and even highly accurate solution, while algorithms without generating a good initial point may probably fail.

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Acknowledgements

Chengjing Wang thanks Professors Defeng Sun and Kim-Chuan Toh at the National University of Singapore for valuable discussions on this paper during his stint in Singapore. Many thanks also go to Dr. Saïd Moussaoui at the Ecole Centrale de Nantes for sharing with us his Matlab code and for fruitful discussions. Finally, we thank the two anonymous referees and the Editor-in-chief Professor Franco Giannessi for their helpful comments and suggestions which improved the quality of this paper.

Chengjing Wang’s work was supported by the National Natural Science Foundation of China under grant 11201382, the Youth Fund of Humanities and Social Sciences of the Ministry of Education under grant 12YJC910008 and the Fundamental Research Funds for the Central Universities under grants SWJTU12CX055 and SWJTU12ZT15.

Aimin Xu’s work was supported by the National Natural Science Foundation of China under grant 11201430, the Zhejiang Province Natural Science Foundation under grant Y6110310, the Research Funds of the Education Department of Zhejiang Province under grant Y201016720, and the Ningbo Natural Science Foundation under grant 2012A610036.

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Authors and Affiliations

  1. School of Mathematics and Institute of Applied Mathematics, Southwest Jiaotong University, Chengdu, 610031, China

    Chengjing Wang

  2. Institute of Mathematics, Zhejiang Wanli University, Ningbo, 315100, China

    Aimin Xu

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  1. Chengjing Wang
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  2. Aimin Xu
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Correspondence to Aimin Xu.

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Wang, C., Xu, A. An Inexact Accelerated Proximal Gradient Method and a Dual Newton-CG Method for the Maximal Entropy Problem. J Optim Theory Appl 157, 436–450 (2013). https://doi.org/10.1007/s10957-012-0150-2

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