From d0607989585f032bc904c79f59023beb79cf052c Mon Sep 17 00:00:00 2001 From: stevenj Date: Mon, 10 Nov 2008 19:57:39 -0500 Subject: [PATCH] fix description of constrained nelder-mead darcs-hash:20081111005739-c8de0-8919dcdbd8209909021bd4148471600a6430ad2b.gz --- neldermead/README | 28 ++++++++++++++++------------ 1 file changed, 16 insertions(+), 12 deletions(-) diff --git a/neldermead/README b/neldermead/README index bcabe30..5dc62d6 100644 --- a/neldermead/README +++ b/neldermead/README @@ -22,17 +22,21 @@ constraints, using essentially the method described in: J. A. Richardson and J. L. Kuester, "The complex method for constrained optimization," Commun. ACM 16(8), 487-489 (1973). -Whenever a new point would lie outside the bound constraints, -Richardson and Kuester advocate moving it "just inside" the -constraints. I couldn't see any advantage to using a fixed distance -inside the constraints, especially if the optimum is on the -constraint, so instead I move the point exactly onto the constraint in -that case. + implementing the method described by: + + M. J. Box, "A new method of constrained optimization and a + comparison with other methods," Computer J. 8 (1), 42-52 (1965). + +Whenever a new point would lie outside the bound constraints, Box +advocates moving it "just inside" the constraints. I couldn't see any +advantage to using a fixed distance inside the constraints, especially +if the optimum is on the constraint, so instead I move the point +exactly onto the constraint in that case. The danger with implementing bound constraints in this way (or by -Richardson and Kuester's method) is that you may collapse the simplex -into a lower-dimensional subspace. I'm not aware of a better way, -however. In any case, this collapse of the simplex is ameliorated by +Box's method) is that you may collapse the simplex into a +lower-dimensional subspace. I'm not aware of a better way, however. +In any case, this collapse of the simplex is ameliorated by restarting, such as when Nelder-Mead is used within the Subplex algorithm below. @@ -78,9 +82,9 @@ be quite close (within 10% for most problems). The only major difference between my implementation and Rowan's, as far as I can tell, is that I implemented explicit support for bound -constraints (via the method in the Richardson and Kuester paper cited -above). This seems to be a big improvement in the case where the -optimum lies against one of the constraints. +constraints (via the method in the Box paper as described above). +This seems to be a big improvement in the case where the optimum lies +against one of the constraints. ----------------------------------------------------------------------- -- 2.30.2