Re: Re: Happy with v. 5.1.1. --- NMinimize, and MathOptimizer Professional
- To: mathgroup at smc.vnet.net
- Subject: [mg55792] Re: [mg55693] Re: [mg55670] Happy with v. 5.1.1. --- NMinimize, and MathOptimizer Professional
- From: "Janos D. Pinter" <jdpinter at hfx.eastlink.ca>
- Date: Wed, 6 Apr 2005 03:11:31 -0400 (EDT)
- References: <200504020628.BAA10750@smc.vnet.net> <200504030951.FAA15751@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Colleagues, For clarity, let me just add a positive note: after increasing the global search effort (from its the default value), MathOptimizer and MathOptimizer Pro both find the solution in Trefethen's 4th problem to the required 10-digit accuracy. This fact is noted also in the book "The SIAM 100-Digit Challenge: A Study in High-Accuracy Numerical Computing", by Folkmar Bornemann · Dirk Laurie · Stan Wagon · Jörg Waldvogel. See http://www-m8.ma.tum.de/m3/bornemann/challengebook/ the site includes Mathematica code for this problem, as well as for the others. Regards, Janos D. Pinter PCS Inc. E-mail: jdpinter at hfx.eastlink.ca Web: www.pinterconsulting.com At 06:51 AM 4/3/2005, Janos D. Pinter wrote: >At 02:28 AM 4/2/2005, Skirmantas wrote: > > >I'm greatly pleased with the new version of NMinimize in Mathematica > >5.1.1. For some reason, NMinimize was working worse in 5.1.0 than in > >5.0.0. (and I complained about it here). Now, in 5.1.1., it again produces > >excellent results. It is more than a minor upgrade; your 5.1.1. NMinimize > >may produce different (hopefully, better) results than 5.1.0. NMinimize. > >__________________________ > > >Skirmantas and others who may be interested, > >Indeed, NMinimize has been greatly improved since its introduction in v. >4.2 (if I recall well). At the same time, let me point out that the model >class addressed by NMinimize (mixed integer nonlinear optimization) >includes very difficult problems, and no solver is perfect to handle 'all' >such models, especially not so in its default operational mode. > >To illustrate this point, consider e.g. Trefethen's Problem 4 > >minimize Exp[Sin[50*x]] + Sin[60*Exp[y]] + Sin[70*Sin[x]] + Sin[Sin[80*y]] >- Sin[10*(x + y)] + (x^2 + y^2)/4 >(w/o stating explicit variable bounds). > >Solving this model by NMinimize and the third party application >MathOptimizer Professional (both used in default solver mode), and applying >the tentative variable bounds [-1,1], [-10,10], [-100,100], one can verify >that 1) neither solves the model to the known global optimum, and 2) >MathOptimizer Professional consistently finds a better quality solution >than NMinimize, for this particular problem. > >The solutions found are: > >NMinimize >{-2.8503166859007303, {x -> -0.02541875771380319, y -> 0.2901752668435903}} >{-2.2781355618824097, {x -> -1.5338718828334104, y -> 0.36797859719983905}} >{-1.8567821476829507, {x -> 0.34251420810742605, y -> 0.5084031754711565}} > >MathOptimizer Professional >{-3.1440794103113316, {x -> -0.0231677651, y -> -0.4942128768}} >{-3.1440794103103786, {x -> -0.0231677607, y -> -0.4942128585}} >{-2.966665564173799, {x -> 0.242806842, y -> -0.0933238715}} > >The true global solution is >(see e.g. http://web.comlab.ox.ac.uk/oucl/work/nick.trefethen/hundred.html >and >http://mathworld.wolfram.com/Hundred-DollarHundred-DigitChallengeProblems.html) >-3.306868647 4752372800 7611377089 8515657166... > >Interested colleagues may like to check out our paper, written with Frank >Kampas, that just appeared in Mathematica in Education in Research 10 >(2005) 2, 1-18. (http://www.ijournals.net). In this work, we present a >systematic comparisons between NMinimize and MathOptimizer Professional in >solving several (uniform and non-uniform size) circle packing models. These >and similar difficult global optimization problems can pretty well and soon >'humble' any numerical optimization package, as the model-size (here: the >number of circles) increases. > >Janos D. Pinter >PCS Inc. >E-mail: jdpinter at hfx.eastlink.ca >Web: www.pinterconsulting.com > > > > >-- >No virus found in this outgoing message. >Checked by AVG Anti-Virus. >Version: 7.0.308 / Virus Database: 266.9.1 - Release Date: 4/1/2005 > > > > >-- >No virus found in this incoming message. >Checked by AVG Anti-Virus. >Version: 7.0.308 / Virus Database: 266.9.1 - Release Date: 4/1/2005 -- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.308 / Virus Database: 266.9.2 - Release Date: 4/5/2005
- References:
- Happy with v. 5.1.1.
- From: Skirmantas <skirmantas.janusonis@yale.edu>
- Re: Happy with v. 5.1.1. --- NMinimize, and MathOptimizer Professional
- From: "Janos D. Pinter" <jdpinter@hfx.eastlink.ca>
- Happy with v. 5.1.1.