Re: Constrained Optimization

*To*: mathgroup at smc.vnet.net*Subject*: [mg57674] Re: Constrained Optimization*From*: Bill Rowe <readnewsciv at earthlink.net>*Date*: Fri, 3 Jun 2005 05:35:01 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

On 6/2/05 at 5:16 AM, seckendorff at alphatec.de (Caspar von Seckendorff) wrote: >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] >As a result I get: "The objective function (x-x^2) y contains a >nonconstant expression y independent of variables {x}." You can avoid this error by adding y as one of the parameters to be maximized, i.e., doing Maximize[{f[x, y], 1/5 <= x <= 2/5, y > 0}, {x,y}] But this won't be any better since the constraints you've given aren't adequate to determine a maximum. (For any value of x satisfying your constraints, f increases linearly with y without bound.) >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? You can achieve the same result by doing Maximize[{f[x, y], 1/5 <= x <= 2/5, y == 0}, {x,y}] or Maximize[{f[x, 1], 1/5 <= x <= 2/5}, x] -- To reply via email subtract one hundred and four