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Global Optimality Conditions in Nonconvex Optimization

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Abstract

In this paper, we address the nonconvex optimization problem, with the goal function and the inequality constraints given by the functions represented by the difference of convex functions. The effectiveness of the classical Lagrange function and the max-merit function is being investigated as the merit functions of the original problem. In addition to the classical apparatus of optimization theory, we apply the new global optimality conditions for the auxiliary problems related to the Lagrange and max-merit functions.

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Acknowledgements

This work has been supported by the Russian Science Foundation, project No. 15-11-20015. The author expresses his particular gratitude to a reviewer whose remarks allowed to improve considerably the presentation of the paper.

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Authors and Affiliations

  1. Matrosov Institute for System Dynamics and Control Theory SB RAS, Lermontov St., 134, Irkutsk, Russia, 664033

    Alexander S. Strekalovsky

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  1. Alexander S. Strekalovsky
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Correspondence to Alexander S. Strekalovsky.

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Communicated by Asen L. Dontchev.

This paper is dedicated to the memory of Vladimir F. Demyanov.

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Strekalovsky, A.S. Global Optimality Conditions in Nonconvex Optimization. J Optim Theory Appl 173, 770–792 (2017). https://doi.org/10.1007/s10957-016-0998-7

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  • DOI: https://doi.org/10.1007/s10957-016-0998-7

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