Abstract
We present an efficient approach to solve resource allocation problems with a single resource, a convex separable objective function, a convex separable resource-usage constraint, and variables that are bounded below and above. Through a combination of function evaluations and median searches, information on whether or not the upper- and lowerbounds are binding is obtained. Once this information is available for all upper and lower bounds, it remains to determine the optimum of a smaller problem with unbounded variables. This can be done through a multiplier search procedure. The information gathered allows for alternative approaches for the multiplier search which can reduce the complexity of this procedure.
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We thank Dick den Hertog and John Einmahl for helpful suggestions.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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De Waegenaere, A., Wielhouwer, J.L. A breakpoint search approach for convex resource allocation problems with bounded variables. Optim Lett 6, 629–640 (2012). https://doi.org/10.1007/s11590-011-0288-0
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DOI: https://doi.org/10.1007/s11590-011-0288-0