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 Tips and Techniques: Nonlinear Fit, Optimization, and the DirectSearch PackageJSFHRobert J. LopezEmeritus Professor of Mathematics and Maple FellowMaplesoftJSFHJSFH
<Text-field style="Heading 1" layout="Heading 1">Introduction</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=In this month's article, I revisit a nonlinear curve-fitting problem that appears in my Advanced Engineering Mathematics ebook, examine the role of Maple's Optimization package in that problem, and then explore the DirectSearch package from Dr. Sergey N. Moiseev.The nonlinear curve-fitting problem was brought to me by one of the statisticians at the Rose-Hulman Institute of Technology well before my 2003 retirement from the classroom. Originating in the newly established biomed faculty at RHIT, its experimentally obtained data points were to be fit by the Michaelis-Menton function 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.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=When I initially examined the problem in Maple V Release 4, I found that the fit command in the (now deprecated) stats package only applied to linear models. Hence, when this problem became a section in the 2001 Addison-Wesley version of my Advanced Engineering Math text, it was solved from first principles by forming and minimizing LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjU1NGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn, the sum of squares of deviations. Since the text predated the Optimization package, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjU1NGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn was minimized by techniques of the calculus. (The essence of the discussion in the text is a comparison between the nonlinear fit and two different linearizations. The linearizations prove to be poor fits!)LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=By the time the AEM ebook was prepared in Maple 10, the Optimization package had been added to Maple, and its use for this problem was then included in the ebook. The results for the minimization of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjU1NGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn, as one would expect, agree for the two approaches. Moreover, the NonlinearFit command in the Statistics package (new in Maple 10) provided an immediate fit of the Michaelis-Menton model to the given data.The recent announcement in MaplePrimes of version 2 of the DirectSearch package caught my attention. I was curious to see to what extent this package would have been of use for the curve-fitting problem in the AEM ebook. I was surprised (and delighted) to discover how robust this package actually is.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 1" layout="Heading 1">Michaelis-Menton Fit to Biomed Data</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Figure 1 is a graph of the 46 data points that are to be fit with the Michaelis-Menton function 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. The plot command and the actual data are "behind" the table containing the graph. To see them, select the "Show input" option in the Table Properties dialog. The data, 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, are given in floating-point form, to six places.JSFH
JSFHThe following definition of the Michaelis-Menton function also takes place in a table for which the input is not shown.JSFH
f := s -> a*s/(b+s):
'f'(s) = f(s);
Prior to Maple 10, there was no direct functionality for a nonlinear fit in Maple. Hence, from first principles, we let LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjU1NGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn be the sum of squares of deviations for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInNGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== and the given data: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(); # input placeholderJSFHFigure 2 is a graph of a portion of the surface LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEjU1NGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Ji1GLDYlUSJhRidGL0YyLUkjbW9HRiQ2LVEiLEYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSJiRidGL0YyRkFGQUZB. It shows the existence of a minimum point, and also shows that this minimum occurs in a steep, but narrow, "valley." Again, the graph appears in a table that conceals input.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
plot3d(SS,a=1..5,b=0..9,axes=box,view=0..10,style=patchcontour, labels=[a,b,"SS"], tickmarks=[5,4,5], orientation=[50,65]);Figure 2 The sum of squares of the deviations graphed as a function of the parameters LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=
JSFHThe ordinary tools of the calculus provide the minimizing values of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=,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print(); # input placeholderJSFHand hence of the fitting function itselfLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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 = print(); # input placeholderJSFHJSFHand the minimum value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjU1NGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn, namely,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 = print(); # input placeholderJSFHJSFHApplying the Optimization package's Minimize command to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjU1NGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn 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(); # input placeholderJSFHThis extreme value is not as accurate as we obtained in . An improvement can be obtained with the Optimization package's NLPSolve command, which became available in Maple 9.5.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print(); # input placeholderJSFHJSFHFrom Maple 10 onwards, the NonlinearFit command from the Statistics package immediately givesLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVErU3RhdGlzdGljc0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIzotRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkwtRiw2JVEtTm9ubGluZWFyRml0RidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNiwtRiw2JVEiZkYnRi9GMi1GUzYkLUYjNiUtRiw2JVEic0YnRi9GMi8lK2V4ZWN1dGFibGVHRj1GOUY5LUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkhGSi9GTlEsMC4zMzMzMzMzZW1GJy1GLDYlUSJTRidGL0YyRl1vLUYsNiVRIlZGJ0YvRjJGXW9GaG5GW29GOUY5LUYsNiNRIUYnRltvRjk=print(); # input placeholderJSFHJSFH
<Text-field style="Heading 1" layout="Heading 1">The <Font italic="true">DirectSearch</Font> Package</Text-field>
<Text-field style="Heading 2" layout="Heading 2">Description</Text-field>JSFHVersion 2 of the DirectSearch package is available from the Maple Application Center. Installation instructions are provided in the README.txt file that accompanies the code. Although written for Maple 13, I've used it in Maple 14 and Maple 15 with no ill effects.The code for the commands in the package are in the archive DirectSearch.mla; the archive DirectSearch.hdb contains the files for the help pages, which are very good. There are three different optimizers: Search, GlobalOptima, and Global Search, all of which use derivative-free direct search methods so all the computations in the package apply to functions that may not be differentiable or continuous. In contrast, the only derivative-free algorithm in Maple's Optimization package is the sequential simplex technique of Nelder and Mead, implemented by the nonlinearsimplex option in the NLPSolve command.For multiobjective optimization, the DirectSearch package has the seven commands Minimax, CompromiseProgramming, WeightedSum, BoundedObjective, ModifiedTchebycheff, WeightedProduct, and ExponentialWeightedSum. In addition, there is the SolveEquations command for solving systems of equations, and the DataFit command for nonlinear fits to data. The DataFit command supports nine different fitting methods, best described via Table 1, extracted from the help page for this command.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
Fit methodMethod descriptionObjective functionlmsLeast mean squares method. This method is effective but not robust to outliers.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 absolute deviations method. This method is more robust to outliers than LMS method.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 trimmed squares method. Robustness of this method depends on upper percentile value p (LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIzk1RidGOUY5 by default).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where TrimmedMean is trimmed meanlwsLeast Winsorized squares method. Robustness of this method depends on upper percentile value p (LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIzk1RidGOUY5 by default).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where WinsorizedMean is Winsorized meanminimaxMinimax method. This method is very sensitive to outliers.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 median squares method. This method is most robust to outliers.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 is sample medianquantileLeast quantile squares method. Robustness of this method depends on quantile order p (LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRJTAuNzVGJ0Y5Rjk= by default).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is sample quantile of order ptrimeanTrimean method. This method is robust to outliers.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 is sample median and quantile of order plfadLeast function of absolute deviations method. Robustness of this method depends on the function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= specified (by default, 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).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Table 1 Options to the DataFit command in the DirectSearch package
<Text-field style="Heading 2" layout="Heading 2">Application 1</Text-field>JSFHOur first application of DirectSearch is to the problem iconized by Figure 1. According to Table 1, the "ordinary" least squares method is implemented in DirectSearch 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print(); # input placeholderJSFHThe first number is the minimum value of the objective function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNidRImFGJy8lJWJvbGRHRjEvRjBRJmZhbHNlRicvRjNRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRkIvRjNRJ25vcm1hbEYnRkVGRQ== defined in the top row of Table 1. Note that this function differs from our LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjU1NGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn by the factor LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIi9GJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHUSV0cnVlRicvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMTY2NjY2N2VtRicvJSdyc3BhY2VHRkgtSSNtaUdGJDYlUSJrRicvJSdpdGFsaWNHRj0vRjBRJ2l0YWxpY0YnRi8=, where, for this calculation, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIzQ2RidGOUY5. Hence, we computeLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW5HRiQ2JFEjNDZGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUScmc2RvdDtGJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkctRiw2JFEzMC4wMzUyNzM0NDgwNzM2OTczRidGLy8lK2V4ZWN1dGFibGVHRjhGLw== = print(); # input placeholderresults compatible with those obtained earlier.JSFH
<Text-field style="Heading 2" layout="Heading 2">Application 2</Text-field>JSFHExercise 3 in Section 47.3 of my Advanced Engineering Mathematics ebook is the isoperimetric problem asking for the extremal LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== that renders a functional LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= stationary, satisfies LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUkjbW5HRiQ2JFEiMEYnL0YzUSdub3JtYWxGJ0Y+Rj4tSSNtb0dGJDYtUSI9RidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRi8lKXN0cmV0Y2h5R0ZGLyUqc3ltbWV0cmljR0ZGLyUobGFyZ2VvcEdGRi8lLm1vdmFibGVsaW1pdHNHRkYvJSdhY2NlbnRHRkYvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZVLUY7NiRRIjFGJ0Y+Rj4=, has arc length LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEiM0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIi9GJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHUSV0cnVlRicvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMTY2NjY2N2VtRicvJSdyc3BhY2VHRkgtRiw2JFEiMkYnRi9GLw==, and intersects the transversal 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, where LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is given byJSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JKG1zdWJzdXBHRiQ2Jy1GNjYtUSsmSW50ZWdyYWw7RidGOS9GPFEmdW5zZXRGJy9GP0ZWL0ZBRjEvRkNGVi9GRUYxL0ZHRlYvRklGVi9GS1EmMC4wZW1GJy9GTkZobi1GIzYnLUkjbW5HRiQ2JFEiMEYnRjlGLy8lK2ZvcmVncm91bmRHUSxbMjAwLDAsMjAwXUYnLyUscGxhY2Vob2xkZXJHRjFGMi1GIzYnLUYsNiVRJyYjOTQ2O0YnL0YwRj1GOUYvRmBvRmNvRjIvJTFzdXBlcnNjcmlwdHNoaWZ0R0Zfby8lL3N1YnNjcmlwdHNoaWZ0R0Zfby1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRInhGJ0YvRjItRjY2LVEiK0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZbcS1GLDYlUSJ5RidGL0YyRjlGOS1GNjYtUSJ+RidGOUY7Rj5GQEZCRkRGRkZIRmduRmluLUY2Ni5RMCZEaWZmZXJlbnRpYWxEO0YnRi9GMkZVRlcvRkFGVkZZL0ZFRlZGZW5GZm5GZ25GaW5GZHBGOQ==JSFHAn extremal LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ==, an arc of the circle 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, is determined by a triple LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNigtSSNtaUdGJDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiLEYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYlUSJiRidGNEY3RjotRjE2JVEnJiM5NDY7RicvRjVGQkY+Rj5GPkY+ that is a solution of the following three equations.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JSFHMaple's fsolve command (numeric solver) finds one solution, namely,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(); # input placeholderUnfortunately, it fails to find any other solution. There is a second solution, found by solving the middle equation for a, and so eliminating a from the first and third equations. This leads to two equations of the form 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, whose graph reveals that there are two intersections of the two implicit functions so defined. The second solution is then found to 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 SolveEquations command in DirectSearch seeks minima of 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, and returns an m \303\227 4 matrix, each row of which details an extreme point: the value of R, a vector of residuals for each LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRImtGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn, the coordinates of the point, and the number of evaluations of R it took to find that point. The minima are arranged in order of increasing value of R. With n = 3, our equations yield the matrixLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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%;LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=which has some 83 rows. The first two solutions areLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYlLUkjbW5HRiQ2JFEiMUYnL0YzUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkYvJSpzeW1tZXRyaWNHRkYvJShsYXJnZW9wR0ZGLyUubW92YWJsZWxpbWl0c0dGRi8lJ2FjY2VudEdGRi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUY7NiRRIjNGJ0Y+Rj4vJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRic=print(); # input 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print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=for which the R-values are on the order of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbW5HRiQ2JFEjMTBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2Ji1JI21vR0YkNi1RKiZ1bWludXMwO0YnRjIvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGTC1GLzYkUSMyMEYnRjIvJSdpdGFsaWNHUSV0cnVlRicvRjNRJ2l0YWxpY0YnLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0Yy and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbW5HRiQ2JFEjMTBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2Ji1JI21vR0YkNi1RKiZ1bWludXMwO0YnRjIvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGTEYuLyUnaXRhbGljR1EldHJ1ZUYnL0YzUSdpdGFsaWNGJy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGMg==, respectively. The value of R in the third row is 1.7 \303\227 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbW5HRiQ2JFEjMTBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2Ji1JI21vR0YkNi1RKiZ1bWludXMwO0YnRjIvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGTC1GLzYkUSI1RidGMi8lJ2l0YWxpY0dRJXRydWVGJy9GM1EnaXRhbGljRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjI=; in the last row it is greater than 7. Hence, we conclude that there are just two solutions of our three equations and these solutions correspond to the two found in Maple.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFH
<Text-field style="Heading 2" layout="Heading 2">Application 3</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Some time ago I was asked if Maple could solve the following set of five equations for 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.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Maple's fsolve command does not provide a solution, and its LSSolve command from the Optimization package gives different solutions (depending on the initial point), generally with sum of squares approximately 3 \303\227 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbW5HRiQ2JFEjMTBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2Ji1JI21vR0YkNi1RKiZ1bWludXMwO0YnRjIvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGTC1GLzYkUSI4RidGMi8lJ2l0YWxpY0dRJXRydWVGJy9GM1EnaXRhbGljRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjI=. I never could bring my self to believe that any of these minima for the sum of squares was actually a solution of the equations.Of course, when I started exploring DirectSearch, I triedLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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%;LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=which results in a 22 \303\227 4 matrix of extrema. The first such extremum, namely,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print(); # input placeholderhas a residual of 9.8 \303\227 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbW5HRiQ2JFEjMTBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2Ji1JI21vR0YkNi1RKiZ1bWludXMwO0YnRjIvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGTC1GLzYkUSI4RidGMi8lJ2l0YWxpY0dRJXRydWVGJy9GM1EnaXRhbGljRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjI=, but no solution produced by SolveEquations matches any returned by LSSolve. The existence of a solution now becomes an urgent issue.To this end, consider the difference LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEoJm1pbnVzO0YnRj4vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkkvJSlzdHJldGNoeUdGSS8lKnN5bW1ldHJpY0dGSS8lKGxhcmdlb3BHRkkvJS5tb3ZhYmxlbGltaXRzR0ZJLyUnYWNjZW50R0ZJLyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGWC1GLDYlRi4tRiM2Iy1GOzYkUSIyRidGPkZAprint(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=It would appear from the difference in signs on the left and right sides of that no solution exists. Hence, we must be careful with numeric "solutions" obtained by minimizing 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. Just because a powerful minimization tool is used does not necessarily mean that a solution has been found for the set of equations 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.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Legal Notice: \302\251 Maplesoft, a division of Waterloo Maple Inc. 2011. 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