Re: Constrained Optimization

*To*: mathgroup at smc.vnet.net*Subject*: [mg57659] Re: [mg57609] Constrained Optimization*From*: "David Park" <djmp at earthlink.net>*Date*: Fri, 3 Jun 2005 05:33:48 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Caspar, Don't you need to maximize over two variables? f[x_, y_] := (x - x^2) y Maximize[{f[x, y], 1/5 <= x <= 2/5, y > 0}, {x, y}] {Infinity, {x -> Indeterminate, y -> Indeterminate}} You still obtain an error message but that is because there is no maximum on the domain. If you restrict the y domain you will obtain a maximum. Maximize[{f[x, y], 1/5 <= x <= 2/5, 0 < y <= 10}, {x, y}] {12/5, {x -> 2/5, y -> 10}} David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ From: Caspar von Seckendorff [mailto:seckendorff at alphatec.de] To: mathgroup at smc.vnet.net 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] 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