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Theoretical filtering of RLT bound-factor constraints for solving polynomial programming problems to global optimality

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  • Evrim Dalkiran
  • Hanif Sherali

Abstract

In this paper, we propose two sets of theoretically filtered bound-factor constraints for constructing reformulation-linearization technique (RLT)-based linear programming (LP) relaxations for solving polynomial programming problems. We establish related theoretical results for convergence to a global optimum for these reduced sized relaxations, and provide insights into their relative sizes and tightness. Extensive computational results are provided to demonstrate the relative effectiveness of the proposed theoretical filtering strategies in comparison to the standard RLT and a prior heuristic filtering technique using problems from the literature as well as randomly generated test cases. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:4:p:1147-1172
    DOI: 10.1007/s10898-012-0024-z
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    References listed on IDEAS

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    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. P. Nataraj & M. Arounassalame, 2011. "Constrained global optimization of multivariate polynomials using Bernstein branch and prune algorithm," Journal of Global Optimization, Springer, vol. 49(2), pages 185-212, February.
    3. Hanif Sherali & Evrim Dalkiran, 2011. "Combined bound-grid-factor constraints for enhancing RLT relaxations for polynomial programs," Journal of Global Optimization, Springer, vol. 51(3), pages 377-393, November.
    4. Faiz A. Al-Khayyal & James E. Falk, 1983. "Jointly Constrained Biconvex Programming," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 273-286, May.
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    2. Brais González-Rodríguez & Raúl Alvite-Pazó & Samuel Alvite-Pazó & Bissan Ghaddar & Julio González-Díaz, 2025. "Polynomial Optimization: Tightening RLT-Based Branch-and-Bound Schemes with Conic Constraints," Journal of Optimization Theory and Applications, Springer, vol. 204(1), pages 1-34, January.
    3. 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.
    4. Boukouvala, Fani & Misener, Ruth & Floudas, Christodoulos A., 2016. "Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO," European Journal of Operational Research, Elsevier, vol. 252(3), pages 701-727.

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