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Semidefinite Program Duals for Separable Polynomial Programs Involving Box Constraints

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Abstract

We show that a separable polynomial program involving a box constraint enjoys a dual problem, that can be displayed in terms of sums of squares univariate polynomials. Under convexification and qualification conditions, we prove that a strong duality relation between the underlying separable polynomial problem and its corresponding dual holds, where the dual problem can be reformulated and solved as a semidefinite programming problem.

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Acknowledgements

The author is grateful to the editor and referee for their valuable comments and suggestions. He is also grateful to Professor V. Jeyakumar for discussing the topic.

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Authors and Affiliations

  1. Optimization and Applications Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Thai Doan Chuong

  2. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Thai Doan Chuong

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  1. Thai Doan Chuong
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Correspondence to Thai Doan Chuong.

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Communicated by Marc Teboulle.

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Chuong, T.D. Semidefinite Program Duals for Separable Polynomial Programs Involving Box Constraints. J Optim Theory Appl 185, 289–299 (2020). https://doi.org/10.1007/s10957-020-01646-5

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  • DOI: https://doi.org/10.1007/s10957-020-01646-5

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