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Computational advances in polynomial optimization: RAPOSa, a freely available global solver

Author

Listed:
  • Brais González-Rodríguez

    (University of Santiago de Compostela
    CITMAga (Galician Centre for Mathematical Research and Technology))

  • Joaquín Ossorio-Castillo

    (CITMAga (Galician Centre for Mathematical Research and Technology))

  • Julio González-Díaz

    (University of Santiago de Compostela
    CITMAga (Galician Centre for Mathematical Research and Technology))

  • Ángel M. González-Rueda

    (University of A Coruña)

  • David R. Penas

    (University of Santiago de Compostela
    CITMAga (Galician Centre for Mathematical Research and Technology))

  • Diego Rodríguez-Martínez

    (CITMAga (Galician Centre for Mathematical Research and Technology))

Abstract

In this paper we introduce RAPOSa, a global optimization solver specifically designed for (continuous) polynomial programming problems with box-constrained variables. Written entirely in C++, RAPOSa is based on the Reformulation-Linearization (Sherali and Tuncbilek in J Glob Optim 103:225–249, 1992). We present a description of the main characteristics of RAPOSa along with a thorough analysis of the impact on its performance of various enhancements discussed in the literature, such as bound tightening and SDP cuts. We also present a comparative study with three of the main state-of-the-art global optimization solvers: BARON, Couenne and SCIP.

Suggested Citation

  • Brais González-Rodríguez & Joaquín Ossorio-Castillo & Julio González-Díaz & Ángel M. González-Rueda & David R. Penas & Diego Rodríguez-Martínez, 2023. "Computational advances in polynomial optimization: RAPOSa, a freely available global solver," Journal of Global Optimization, Springer, vol. 85(3), pages 541-568, March.
    • Handle: RePEc:spr:jglopt:v:85:y:2023:i:3:d:10.1007_s10898-022-01229-w
    DOI: 10.1007/s10898-022-01229-w
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    References listed on IDEAS

    as
    1. Hanif Sherali & Evrim Dalkiran & Jitamitra Desai, 2012. "Enhancing RLT-based relaxations for polynomial programming problems via a new class of v-semidefinite cuts," Computational Optimization and Applications, Springer, vol. 52(2), pages 483-506, June.
    2. Andrea Lodi & Giulia Zarpellon, 2017. "Rejoinder on: On learning and branching: a survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 247-248, July.
    3. Pietro Belotti, 2013. "Bound reduction using pairs of linear inequalities," Journal of Global Optimization, Springer, vol. 56(3), pages 787-819, July.
    4. Hanif Sherali & Evrim Dalkiran & Leo Liberti, 2012. "Reduced RLT representations for nonconvex polynomial programming problems," Journal of Global Optimization, Springer, vol. 52(3), pages 447-469, March.
    5. Andrea Lodi & Giulia Zarpellon, 2017. "On learning and branching: a survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 207-236, July.
    6. Evrim Dalkiran & Hanif Sherali, 2013. "Theoretical filtering of RLT bound-factor constraints for solving polynomial programming problems to global optimality," Journal of Global Optimization, Springer, vol. 57(4), pages 1147-1172, December.
    7. Ambros M. Gleixner & Timo Berthold & Benjamin Müller & Stefan Weltge, 2017. "Three enhancements for optimization-based bound tightening," Journal of Global Optimization, Springer, vol. 67(4), pages 731-757, April.
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