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A method based on parametric convex programming for solving convex multiplicative programming problem

Author

Listed:
  • Yunchol Jong

    (University of Science)

  • Yongjin Kim

    (University of Science)

  • Hyonchol Kim

    (University of Science)

Abstract

We propose a new parametric approach to convex multiplicative programming problem. This problem is nonconvex optimization problem with a lot of practical applications. Compared with preceding methods based on branch-and-bound procedure and other approaches, the idea of our method is to reduce the original nonconvex problem to a parametric convex programming problem having parameters in objective functions. To find parameters corresponding to the optimal solution of the original problem, a system of nonlinear equations which the parameters should satisfy is studied. Then, the system is solved by a Newton-like algorithm, which needs to solve a convex programming problem in each iteration and has global linear and local superlinear/quadratic rate of convergence under some assumptions. Moreover, under some mild assumptions, our algorithm has a finite convergence, that is, the algorithm finds a solution after a finite number of iterations. The numerical results show that our method has much better performance than other reported methods for this class of problems.

Suggested Citation

  • Yunchol Jong & Yongjin Kim & Hyonchol Kim, 2024. "A method based on parametric convex programming for solving convex multiplicative programming problem," Journal of Global Optimization, Springer, vol. 90(3), pages 573-592, November.
    • Handle: RePEc:spr:jglopt:v:90:y:2024:i:3:d:10.1007_s10898-024-01416-x
    DOI: 10.1007/s10898-024-01416-x
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    References listed on IDEAS

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    2. Peiping Shen & Kaimin Wang & Ting Lu, 2020. "Outer space branch and bound algorithm for solving linear multiplicative programming problems," Journal of Global Optimization, Springer, vol. 78(3), pages 453-482, November.
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