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

Hanif D. Sherali and Jitamitra Desai

Chapter Chapter 5 in Essays and Surveys in Global Optimization, 2005, pp 131-163 from Springer

Abstract: 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.

Keywords: Global Optimization; Network Lifetime; Valid Inequality; Semidefinite Programming; Nonconvex Optimization Problem (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-387-25570-5_5

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DOI: 10.1007/0-387-25570-2_5

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