Dyer, M, Kannan, R and Stougie, L (2014) A simple randomised algorithm for convex optimisation: Application to two-stage stochastic programming. Mathematical Programming, 147 (1-2). pp. 207-229. ISSN 0025-5610
Abstract
We consider maximising a concave function over a convex set by a simple randomised algorithm. The strength of the algorithm is that it requires only approximate function evaluations for the concave function and a weak membership oracle for the convex set. Under smoothness conditions on the function and the feasible set, we show that our algorithm computes a near-optimal point in a number of operations which is bounded by a polynomial function of all relevant input parameters and the reciprocal of the desired precision, with high probability. As an application to which the features of our algorithm are particularly useful we study two-stage stochastic programming problems. These problems have the property that evaluation of the objective function is #P-hard under appropriate assumptions on the models. Therefore, as a tool within our randomised algorithm, we devise a fully polynomial randomised approximation scheme for these function evaluations, under appropriate assumptions on the models. Moreover, we deal with smoothing the feasible set, which in two-stage stochastic programming is a polyhedron.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2013. The final publication is available at Springer via http://dx.doi.org/10.1007/s10107-013-0718-0 |
Keywords: | Convex optimisation, Stochastic programming, Randomised algorithms, Polynomial time randomised approximation scheme |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) > Institute for Computational and Systems Science (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 22 Mar 2016 16:35 |
Last Modified: | 20 Jan 2018 21:11 |
Published Version: | http://dx.doi.org/10.1007/s10107-013-0718-0 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s10107-013-0718-0 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:89272 |