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.
Preview
Unable to display preview. Download preview PDF.
References
A. Charnes and C.E. Lemke, “Minimization of nonlinear separable convex functionals,” Naval Research Logistic Quarterly 1 (1954) 301–312.
G.B. Dantzig, Linear programming and extensions (Princeton University Press, Princeton, 1963).
G.B. Dantzig and P. Wolfe, “The decomposition principle for linear programs”, Operations Research 8 (1960) 101–111.
R. Fourer, “Piecewise-linear programming”, Department of Industrial Engineering and Management Science, Northwestern University (1983).
J.K. Ho, “A successive linear optimization approach to the dynamic traffic assignment problem”, Transportation Science 14 (1980) 295–305.
J.K. Ho and E. Loute, “Computational experience with advanced implementation of decomposition algorithms for linear programming”, Mathematical Programming 27 (1983) 283–290.
Author information
Authors and Affiliations
Editor information
Additional information
Dedicated to Professor George B. Dantzig, in celebration of his 70th birthday.
Rights and permissions
Copyright information
© 1985 The Mathematical Programming Society, Inc.
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/BFb0121047
Received:
Revised:
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00918-1
Online ISBN: 978-3-642-00919-8
eBook Packages: Springer Book Archive