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

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Book cover Essays and Surveys in Global Optimization

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.

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Authors
  1. Hanif D. Sherali
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  2. Jitamitra Desai
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Editors and Affiliations

  1. École Polytechnique de Montréal and GERAD, Montréal, Canada

    Charles Audet  & Gilles Savard  & 

  2. HEC Montréal & GERAD, Montréal, Canada

    Pierre Hansen

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Sherali, H.D., Desai, J. (2005). On Solving Polynomial, Factorable, and Black-Box Optimization Problems Using the RLT Methodology. In: Audet, C., Hansen, P., Savard, G. (eds) Essays and Surveys in Global Optimization. Springer, Boston, MA. https://doi.org/10.1007/0-387-25570-2_5

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