On mixed-integer zero-one representations for separable lower-semicontinuous piecewise-linear functions

  • Authors:

  • Hanif D. Sherali

  • Affiliations:

  • Grado Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University, 250 New Engineering Building, Blacksburg, VA 24061, USA

  • Venue:
  • Operations Research Letters
  • Year:
  • 2001

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Abstract

In a recent paper, Padberg (Oper. Res. Lett. 27(1) (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.