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Relationships among linear formulations of separable convex piecewise linear programs

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Mathematical Programming Essays in Honor of George B. Dantzig Part I

Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 24))

Abstract

This paper considers four equivalent methods to linearize separable convex piecewise linear programming problems. These methods lead to different linear programming formulations which are necessarily equivalent in the sense that they imply the same optimal solutions. It is shown that the exact relationships among them can be established through the application of the decomposition principle of Dantzig and Wolfe.

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References

  1. A. Charnes and C.E. Lemke, “Minimization of nonlinear separable convex functionals,” Naval Research Logistic Quarterly 1 (1954) 301–312.

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  4. R. Fourer, “Piecewise-linear programming”, Department of Industrial Engineering and Management Science, Northwestern University (1983).

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R. W. Cottle

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Dedicated to Professor George B. Dantzig, in celebration of his 70th birthday.

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© 1985 The Mathematical Programming Society, Inc.

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Ho, J.K. (1985). Relationships among linear formulations of separable convex piecewise linear programs. In: Cottle, R.W. (eds) Mathematical Programming Essays in Honor of George B. Dantzig Part I. Mathematical Programming Studies, vol 24. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121047

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  • DOI: https://doi.org/10.1007/BFb0121047

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00918-1

  • Online ISBN: 978-3-642-00919-8

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