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Canonical Primal–Dual Method for Solving Nonconvex Minimization Problems

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Canonical Duality Theory

Part of the book series: Advances in Mechanics and Mathematics ((AMMA,volume 37))

Abstract

A new primal–dual algorithm is presented for solving a class of nonconvex minimization problems. This algorithm is based on canonical duality theory such that the original nonconvex minimization problem is first reformulated as a convex–concave saddle point optimization problem, which is then solved by a quadratically perturbed primal–dual method. Numerical examples are illustrated. Comparing with the existing results, the proposed algorithm can achieve better performance.

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Notes

  1. 1.

    In fact, Problem (\(\mathscr {P}\)) is convex under the condition \(\bar{\chi }+\chi \ge 0\). The proof of this result is similar to that of Proposition 1 given in [16].

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Acknowledgements

The research was supported by US Air Force Office of Scientific Research under the grants AFOSR FA9550-17-1-0151 and AOARD FOST-16-265. Numerical computation was performed by research student Mr. Chaojie Li at Federation University.

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Authors and Affiliations

  1. Faculty of Science and Technology, Federation University Australia, Ballarat, VIC, 3353, Australia

    Changzhi Wu

  2. Faculty of Science and Technology, Federation University Australia, Ballarat, VIC, 3353, Australia

    David Yang Gao

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  1. Changzhi Wu
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  2. David Yang Gao
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Correspondence to David Yang Gao .

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Editors and Affiliations

  1. Faculty of Science and Technology, Federation University Australia, Mt. Helen, Victoria, Australia

    David Yang Gao

  2. Department of Computer, Control, and Managment Engineering, Sapienza University of Rome, Rome, Roma, Italy

    Vittorio Latorre

  3. Faculty of Science and Technology, Federation University Australia, Mt. Helen, Victoria, Australia

    Ning Ruan

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Wu, C., Gao, D.Y. (2017). Canonical Primal–Dual Method for Solving Nonconvex Minimization Problems. In: Gao, D., Latorre, V., Ruan, N. (eds) Canonical Duality Theory. Advances in Mechanics and Mathematics, vol 37. Springer, Cham. https://doi.org/10.1007/978-3-319-58017-3_11

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