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Unified Interior Point Methodology for Canonical Duality in Global Optimization

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Canonical Duality Theory

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

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Abstract

We propose an interior point method to solve instances of the nonconvex optimization problems reformulated with canonical duality theory. To this aim we propose an interior point potential reduction algorithm based on the solution of the primal–dual total complementarity function. We establish the global convergence result for the algorithm under mild assumptions. Our methodology is quite general and can be applied to several problems which dual has been formulated with canonical duality theory and shows the possibility of devising efficient interior points methods for nonconvex duality.

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Acknowledgements

The Author would like to thank Simone Sagratella for his help. Without his suggestions in the initial conception of this method, it would have been quite difficult to understand the right path to take in order to create the presented framework. The author would also like to thank Professor Stefano Lucidi for his suggestions for improving the paper.

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Authors and Affiliations

  1. Department of Computer, Control and Management Engineering, “Sapienza”, University of Rome, Via Ariosto 25, 00185, Rome, Italy

    Vittorio Latorre

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  1. Vittorio Latorre
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Correspondence to Vittorio Latorre .

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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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Latorre, V. (2017). Unified Interior Point Methodology for Canonical Duality in Global Optimization. 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_12

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