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A branch-and-bound algorithm for parametric mixed-binary nonlinear programs

Author

Listed:
  • Andrew C. Pangia

    (Clemson University)

  • Margaret M. Wiecek

    (Clemson University)

Abstract

As rapid response to changes becomes more imperative, optimization under uncertainty has continued to grow in both the continuous and mixed-integer fields. We design a branch-and-bound (BB) algorithm for mixed-binary nonlinear optimization problems with parameters in general locations. At every node of the BB tree we apply a state-of-the-art algorithm we have recently developed to approximately optimize parametric programs containing objectives and constraints biconvex in the variables and parameters. Numerical results are included.

Suggested Citation

  • Andrew C. Pangia & Margaret M. Wiecek, 2025. "A branch-and-bound algorithm for parametric mixed-binary nonlinear programs," Journal of Global Optimization, Springer, vol. 91(3), pages 457-481, March.
    • Handle: RePEc:spr:jglopt:v:91:y:2025:i:3:d:10.1007_s10898-024-01447-4
    DOI: 10.1007/s10898-024-01447-4
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    References listed on IDEAS

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    1. Dang Hieu & Pham Ky Anh & Le Dung Muu, 2019. "Modified extragradient-like algorithms with new stepsizes for variational inequalities," Computational Optimization and Applications, Springer, vol. 73(3), pages 913-932, July.
    2. Richard Oberdieck & Martina Wittmann-Hohlbein & Efstratios Pistikopoulos, 2014. "A branch and bound method for the solution of multiparametric mixed integer linear programming problems," Journal of Global Optimization, Springer, vol. 59(2), pages 527-543, July.
    3. Martina Wittmann-Hohlbein & Efstratios Pistikopoulos, 2013. "On the global solution of multi-parametric mixed integer linear programming problems," Journal of Global Optimization, Springer, vol. 57(1), pages 51-73, September.
    4. Pubudu L. W. Jayasekara & Andrew C. Pangia & Margaret M. Wiecek, 2023. "On solving parametric multiobjective quadratic programs with parameters in general locations," Annals of Operations Research, Springer, vol. 320(1), pages 123-172, January.
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