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Solution to Global Minimization of Polynomials by Backward Differential Flow

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Abstract

This paper presents a study on solutions to the global minimization of polynomials. The backward differential flow by the K–T equation with respect to the optimization problem is introduced to deal with a ball-constrained optimization problem. The unconstrained optimization is reduced to a constrained optimization problem which can be solved by a backward differential flow. Some examples are illustrated with an algorithm for computing the backward flow.

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Acknowledgements

This research was partly supported by the National Science Foundation of China under grant No. 10671145.

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Authors and Affiliations

  1. Department of Mathematics, Tongji University, Shanghai, China

    Jinghao Zhu, Shangrui Zhao & Guohua Liu

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  1. Jinghao Zhu
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  2. Shangrui Zhao
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  3. Guohua Liu
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Correspondence to Jinghao Zhu.

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Zhu, J., Zhao, S. & Liu, G. Solution to Global Minimization of Polynomials by Backward Differential Flow. J Optim Theory Appl 161, 828–836 (2014). https://doi.org/10.1007/s10957-013-0388-3

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  • DOI: https://doi.org/10.1007/s10957-013-0388-3

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