| Author |
Comment/Response |
Randy Silvers
|
 05/18/08 04:20am
With Maximize and NMaximize and FindMaximum, you can also specify the optimization algorithm -- Gradient is one such.
Also, look at NestWhile or FixedPoint. You can define a way to alter the choice variable t and iterate using NestWhile.
A good source for different types of numerical algorithms is available at http://math.fullerton.edu/mathews/n2003/Web/NumericalModules.html
One such algorithm that does not compute derivatives, but works if the function is concave, is to start with a large interval (x0, x1) that contains the maximum. Suppose w.l.g. that the function value is greater at x1 than at x0. Now, compute two intermediate values and the function values at each of those, f[mid1] and f[mid2]. If f[mid1]<f[mid2], then the maximum is attained somewhere in [mid1,x1] since the function is decreasing on (x0,mid1).
See attached, which implements this algorithm to derive the optimal output of a duopolist given the other firm's output.
Attachment: nasheq.nb, URL: sirandol@deakin.edu.au, |
|
