dc.contributor.author | Raghavachari, M. | |
dc.date.accessioned | 2010-07-23T10:06:50Z | |
dc.date.available | 2010-07-23T10:06:50Z | |
dc.date.copyright | 1977 | |
dc.date.issued | 1977-07-23T10:06:50Z | |
dc.identifier.citation | Mathematical Programming, Dec-1977, Vol.13(1), pp 156–166 | en |
dc.identifier.uri | http://hdl.handle.net/11718/6106 | |
dc.description.abstract | Let @p be the set of all doubly stochastic square matrices of order p i.e. the set of all p × p
matrices with non-negative entries with row and column sums equal to unity. The permanent
of a p × p matrix A = (aij) is defined by P(A)= ]~,esplI~=t ai~,) where Sp is the symmetric
group of order p. Van der Waerden conjectured that P(A) >~ p ![p p for all A E ~p with equality
occurring if and only if A = Jp, where Yp is the matrix all of whose entries are equal to 1/p.
The validity of this conjecture has been shown for a few values of p and for general p
under certain assumptions. In this paper the problem of finding the minimum of the permanent
of a doubly stochastic matrix has been formulated as a reversed geometric program with a
single constraint and an equivalent dual program is given. A related problem of reversed
homogeneous posynomial programming problem is also studied. | |
dc.language.iso | en | en |
dc.title | A geometric programming approach to the Van der Waerden conjecture on doubly stochastic matrices | en |
dc.type | Article | en |