dc.contributor.author | Mittal, Shashi | |
dc.contributor.author | Schulz, Andreas S. | |
dc.date.accessioned | 2013-01-17T14:41:48Z | |
dc.date.available | 2013-01-17T14:41:48Z | |
dc.date.issued | 2012-01 | |
dc.date.submitted | 2010-12 | |
dc.identifier.issn | 0025-5610 | |
dc.identifier.issn | 1436-4646 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/76278 | |
dc.description.abstract | We present a fully polynomial time approximation scheme (FPTAS) for optimizing a very general class of non-linear functions of low rank over a polytope. Our approximation scheme relies on constructing an approximate Pareto-optimal front of the linear functions which constitute the given low-rank function. In contrast to existing results in the literature, our approximation scheme does not require the assumption of quasi-concavity on the objective function. For the special case of quasi-concave function minimization, we give an alternative FPTAS, which always returns a solution which is an extreme point of the polytope. Our technique can also be used to obtain an FPTAS for combinatorial optimization problems with non-linear objective functions, for example when the objective is a product of a fixed number of linear functions. We also show that it is not possible to approximate the minimum of a general concave function over the unit hypercube to within any factor, unless P = NP. We prove this by showing a similar hardness of approximation result for supermodular function minimization, a result that may be of independent interest. | en_US |
dc.language.iso | en_US | |
dc.publisher | Springer-Verlag | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1007/s10107-011-0511-x | en_US |
dc.rights | Creative Commons Attribution-Noncommercial-Share Alike 3.0 | en_US |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/3.0/ | en_US |
dc.source | MIT web domain | en_US |
dc.title | An FPTAS for optimizing a class of low-rank functions over a polytope | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Mittal, Shashi, and Andreas S. Schulz. “An FPTAS for Optimizing a Class of Low-rank Functions over a Polytope.” Mathematical Programming (2012). | en_US |
dc.contributor.department | Sloan School of Management | en_US |
dc.contributor.mitauthor | Schulz, Andreas S. | |
dc.relation.journal | Mathematical Programming | en_US |
dc.eprint.version | Author's final manuscript | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dspace.orderedauthors | Mittal, Shashi; Schulz, Andreas S. | en |
dc.identifier.orcid | https://orcid.org/0000-0002-9595-459X | |
mit.license | OPEN_ACCESS_POLICY | en_US |
mit.metadata.status | Complete | |