期刊
OPERATIONS RESEARCH LETTERS
卷 28, 期 4, 页码 155-160出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/S0167-6377(01)00063-3
关键词
zero-one modeling; piecewise-linear approximations; separable nonlinear programs; locally ideal formulations
In a recent paper, Padberg (Oper. Res. Lett. 27(l) (2000) 1) has provided some insights into constructing locally ideal formulations for continuous piecewise-linear approximations to separable nonlinear programs. He shows that in contrast with such representations, the standard text-book modeling strategy is weak with respect to its linear programming relaxation. We propose a new pedagogically simpler modification of the latter formulation that constructs its convex hull representation, thereby rendering it locally ideal. Moreover, this modeling strategy imparts a totally unimodular structure to the formulation, it readily extends to representing separable lower-semicontinuous piecewise-linear functions, and it also facilitates a reduced locally ideal representation based on a piecewise-linear convex decomposition of the function. In the special case of continuous piecewise-linear functions, we exhibit a nonsingular linear transformation that equivalently converts the proposed model into Padberg's formulation. (C) 2001 Published by Elsevier Science B.V.
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