An algorithm for approximating piecewise linear concave functions from sample gradients

Authors:
Huseyin Topaloglu;Warren B. Powell
Affiliations:
Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ 08544, USA;Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ 08544, USA
Venue:
Operations Research Letters
Year:
2003

Citing 6
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Abstract

An effective algorithm for solving stochastic resource allocation problems is to build piecewise linear, concave approximations of the recourse function based on sample gradient information. Algorithms based on this approach are proving useful in application areas such as the newsvendor problem, physical distribution and fleet management. These algorithms require the adaptive estimation of the approximations of the recourse function that maintain concavity at every iteration. In this paper, we prove convergence for a particular version of an algorithm that produces approximations from stochastic gradient information while maintaining concavity.