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Global Optimality Conditions in Nonconvex Optimization

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  • Alexander S. Strekalovsky

    (Matrosov Institute for System Dynamics and Control Theory SB RAS)

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.

Suggested Citation

  • Alexander S. Strekalovsky, 2017. "Global Optimality Conditions in Nonconvex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 173(3), pages 770-792, June.
    • Handle: RePEc:spr:joptap:v:173:y:2017:i:3:d:10.1007_s10957-016-0998-7
    DOI: 10.1007/s10957-016-0998-7
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    References listed on IDEAS

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    1. Alexander S. Strekalovsky, 2013. "Global Optimality Conditions for Optimal Control Problems with Functions of A.D. Alexandrov," Journal of Optimization Theory and Applications, Springer, vol. 159(2), pages 297-321, November.
    2. Strekalovsky, Alexander S., 2015. "On local search in d.c. optimization problems," Applied Mathematics and Computation, Elsevier, vol. 255(C), pages 73-83.
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    Cited by:

    1. Gruzdeva, Tatiana V. & Strekalovsky, Alexander S., 2018. "On solving the sum-of-ratios problem," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 260-269.
    2. M. V. Dolgopolik, 2020. "New global optimality conditions for nonsmooth DC optimization problems," Journal of Global Optimization, Springer, vol. 76(1), pages 25-55, January.

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