Re: Constrained Optimization

*To*: mathgroup at smc.vnet.net*Subject*: [mg57675] Re: Constrained Optimization*From*: dh <dh at metrohm.ch>*Date*: Fri, 3 Jun 2005 05:35:04 -0400 (EDT)*References*: <d7mj30$bqm$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi Caspar, see below. sincerely, Daniel Caspar von Seckendorff wrote: > Hi, > > I'd like to do constrained optimization with Mathematica 5.1 on a > function that is defined piecewise. Unfortunately Maximize[] does not > work as I expected. A short & simple example to illustrate: > > f[x_,y_]:= (x-x^2) y > Maximize[{f[x, y], 1/5 <= x <= 2/5, y > 0}, x] Maximize is a numerical functions. Therefore, f[,] needs numeric input. However, y is so far a puer symbol and has no numerical value. If I understand your problem correctly, y is assumed to be a constant. But in this case the maximum value depends on the unspecified y. Mathematica gives you a correct error message. > > As a result I get: > "The objective function (x-x^2) y contains a nonconstant expression y > independent of variables {x}." > > Obviously for this Maximization, knowing that y > 0 I can do the > following to get the desired value for x: > > Maximize[{x-x^2, 1/5 <= x <= 2/5}, x] > Out[]= {6/25, {x -> 2/5}} > > Is there a way to achieve this without manual intervention? The reason > is, that the functions I want to Maximize are defined Piecewise with > several constraints... > > Thanks, > > -Caspar >