MINIMIZATION USING THE SIMPLEX METHOD FROM MATLAB

 

Professor Lyndell Kerley and Jeff Knisley, East Tennessee State University

 

Matlab has a feature which minimizes a function of several variables.

 

We wish to minimize the function R = bWa as described in Burden and Faires, Numerical Analysis, 6th ed on p 486. The problem is based on a paper dealing with the efficiency of energy utilization of the larvae of the modest sphinx moth (Pachysphinx modesta), Schroeder, L. A., Energy budget of the larvae of the moth Pachysphinx modesta, Oikos 24(1973), 278-281, QH540.O35 486. Data was used to determine a relationship between the two variables W and R. W is the live weight of the larvae in grams and R is the oxygen consumption of the larvae in milliliters/hours. For biological reasons, it is assumed that a relationship in the form of R = bWa exists between W and R.

 

Three files data d486.m , e.m,  approx.m at ftp://ftp.etsu.edu/pubdata/kerleyl/primus/ minimize the function R = bWa.  This is achieved by using the built-in function FMINS available in matlab. See help FMINS in the matlab environment for a discussion.

 

The following output is obtained upon running the program approx.m.

 

» approx

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*************Linear and quadratic regression****************

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Coefficients using linear regression

 

soln =

 

   0.26464763861898

   0.57564260277249

 

Error using least sq poly after using log = 25.3018

Coefficients using quadratic regression

 

soln =

 

   0.04962021353237

   0.70062918760672

   0.06695491979366

 

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*********Technique using Nelder-Mead simplex (direct search) method*******

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Coefficients a and b where R = bW^a using simplex method

 

Minimum =

 

   0.75022215038798

   1.18466540633574

 

Smaller error using simplex method = 19.7961

»

blue is linear approximation, yellow is quadratic approximation, and green is simplex method approximation all overlaying the data from data486.m