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On Solving Polynomial, Factorable, and Black-Box Optimization Problems Using the RLT Methodology

In: Essays and Surveys in Global Optimization

Author

Listed:
  • Hanif D. Sherali
  • Jitamitra Desai

Abstract

This paper provides an expository discussion on using the Reformulation-Linearization/Convexification (RLT) technique as a unifying approach for solving nonconvex polynomial, factorable, and certain black-box optimization problems. The principal RLT construct applies a Reformulation phase to add valid inequalities including polynomial and semidefinite cuts, and a Linearization phase to derive higher dimensional tight linear programming relaxations. These relaxations are embedded within a suitable branch-and-bound scheme that converges to a global optimum for polynomial or factorable programs, and results in a pseudo-global optimization method that derives approximate, near-optimal solutions for black-box optimization problems. We present the basic underlying theory, and illustrate the application of this theory to solve various problems.

Suggested Citation

  • Hanif D. Sherali & Jitamitra Desai, 2005. "On Solving Polynomial, Factorable, and Black-Box Optimization Problems Using the RLT Methodology," Springer Books, in: Charles Audet & Pierre Hansen & Gilles Savard (ed.), Essays and Surveys in Global Optimization, chapter 0, pages 131-163, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-25570-5_5
    DOI: 10.1007/0-387-25570-2_5
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    Citations

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    Cited by:

    1. M Laguna & J Molina & F Pérez & R Caballero & A G Hernández-Díaz, 2010. "The challenge of optimizing expensive black boxes: a scatter search/rough set theory approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(1), pages 53-67, January.
    2. Jitamitra Desai & Shalinee Kishore, 2017. "A global optimization framework for distributed antenna location in CDMA cellular networks," Annals of Operations Research, Springer, vol. 253(1), pages 169-191, June.
    3. Teles, João P. & Castro, Pedro M. & Matos, Henrique A., 2013. "Univariate parameterization for global optimization of mixed-integer polynomial problems," European Journal of Operational Research, Elsevier, vol. 229(3), pages 613-625.

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