Re: Re: Smallest enclosing circle

*To*: mathgroup at smc.vnet.net*Subject*: [mg50153] Re: [mg50142] Re: Smallest enclosing circle*From*: "Janos D. Pinter" <jdpinter at hfx.eastlink.ca>*Date*: Wed, 18 Aug 2004 01:20:00 -0400 (EDT)*References*: <cfi8tm$4p6$1@smc.vnet.net> <200408140550.BAA15340@smc.vnet.net> <cfomej$kul$1@smc.vnet.net> <200408170901.FAA09939@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

At 06:01 AM 8/17/2004, Ray Koopman wrote: >DrBob <drbob at bigfoot.com> wrote in message news:<cfomej$kul$1 at smc.vnet.net>... > > Finally! > > > > NMinimize does a better job than FindMinimum, and constraints are not > needed: > > > > [...] > >I agree. FindMinimum is not trustworthy here: it's usually close, >but not close enough, and increasing AccuracyGoal and PrecisionGoal >doesn't help. NMinimize does not have this problem. The same applies also for the (global scope) MathOptimizer and MathOptimizer Professional solver systems. These can be (and have been) used to solve far more difficult configuration design problems such as e.g. finding the minimal radius circle that includes a set of non-uniform size, non-overlapping circles. Some of our related results will appear in The Mathematica Journal, issue 4 of 2004. If someone wishes to solve the same problem with any other optimization tool available for Mathematica (incl. also NMinimize), then Frank Kampas and myself will be much interested in the results. We have produced comparative numerical results for embedded circle radii r_i=1/(i)^0.5, i=1,..,imax for up to imax=40. Regards, Janos Pinter

**References**:**Re: Smalest enclosing circle***From:*kzhang@flashmail.com (Kezhao Zhang)

**Re: Smalest enclosing circle***From:*koopman@sfu.ca (Ray Koopman)