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On local search in d.c. optimization problems

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  • Strekalovsky, Alexander S.

Abstract

First, we consider a d.c. minimization problem with a simple feasible set and develop a special method based on the linearization with respect to the basic nonconvexity. The convergence of the methods is analyzed and compared with published results. Theoretical and practical stopping criteria are proposed. Second, we consider a problem with d.c. constraint and study the properties of special local search method for this problem. Finally, we consider a variant of local search for a general d.c. optimization problem and investigate its convergence.

Suggested Citation

  • Strekalovsky, Alexander S., 2015. "On local search in d.c. optimization problems," Applied Mathematics and Computation, Elsevier, vol. 255(C), pages 73-83.
    • Handle: RePEc:eee:apmaco:v:255:y:2015:i:c:p:73-83
    DOI: 10.1016/j.amc.2014.08.092
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    References listed on IDEAS

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    1. Le An & Pham Tao, 2005. "The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems," Annals of Operations Research, Springer, vol. 133(1), pages 23-46, January.
    2. Alexander Strekalovsky & Andrey Orlov & Anton Malyshev, 2010. "On computational search for optimistic solutions in bilevel problems," Journal of Global Optimization, Springer, vol. 48(1), pages 159-172, September.
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    Cited by:

    1. Sinha, Ankur & Das, Arka & Anand, Guneshwar & Jayaswal, Sachin, 2021. "A General Purpose Exact Solution Method for Mixed Integer Concave Minimization Problems," IIMA Working Papers WP 2021-03-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    2. Sinha, Ankur & Das, Arka & Anand, Guneshwar & Jayaswal, Sachin, 2023. "A general purpose exact solution method for mixed integer concave minimization problems," European Journal of Operational Research, Elsevier, vol. 309(3), pages 977-992.
    3. Alexander S. Strekalovsky, 2017. "Global Optimality Conditions in Nonconvex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 173(3), pages 770-792, June.
    4. 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.
    5. Sinha, Ankur & Das, Arka & Anand, Guneshwar & Jayaswal, Sachin, 2021. "A General Purpose Exact Solution Method for Mixed Integer Concave Minimization Problems (revised as on 12/08/2021)," IIMA Working Papers WP 2021-03-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    6. Mikhail Posypkin & Oleg Khamisov, 2021. "Automatic Convexity Deduction for Efficient Function’s Range Bounding," Mathematics, MDPI, vol. 9(2), pages 1-16, January.
    7. Joki, Kaisa & Bagirov, Adil M. & Karmitsa, Napsu & Mäkelä, Marko M. & Taheri, Sona, 2020. "Clusterwise support vector linear regression," European Journal of Operational Research, Elsevier, vol. 287(1), pages 19-35.
    8. Wim Ackooij & Welington Oliveira, 2019. "Nonsmooth and Nonconvex Optimization via Approximate Difference-of-Convex Decompositions," Journal of Optimization Theory and Applications, Springer, vol. 182(1), pages 49-80, July.
    9. S. Dempe & S. Franke, 2016. "On the solution of convex bilevel optimization problems," Computational Optimization and Applications, Springer, vol. 63(3), pages 685-703, April.

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