Abstract
We consider the problem of finding a minimum along a given direction d∈ℝm, of a separable function ά(χ)=Σ ml=1 ψ l (χ l ). Each component ψ l (χ l ) is a piecewise-linear convex function expressed in slope-intercept form. To solve this problem we propose a specialized version of the generalized upper bounding (GUB) algorithm of Dantzig and Van Slyke. Each step of the simplex cycle is explicitly expressed as a simple algebraic formula and basis matrix operations are completely eliminated. This results in a concise, elegant and efficient algorithm.
This research was carried out at the International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria.
Present address: Computational Decision Support Systems, P.O. Box 4908, Berkeley, CA 94704, USA.
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Dedicated to Professor George B. Dantzig on the occasion of his seventieth birthday.
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© 1985 The Mathematical Programming Society, Inc.
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Nazareth, J.L. (1985). An efficient algorithm for minimizing a multivariate polyhedral function along a line. 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/BFb0121046
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DOI: https://doi.org/10.1007/BFb0121046
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Publisher Name: Springer, Berlin, Heidelberg
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