Re: How can I minimize it?
- To: mathgroup at smc.vnet.net
- Subject: [mg94738] Re: How can I minimize it?
- From: dh <dh at metrohm.com>
- Date: Mon, 22 Dec 2008 05:16:50 -0500 (EST)
- References: <gig3qh$2lq$1@smc.vnet.net>
Hi, is your function given analytically and are you actually searching for a Sattle point? If both question are answered with yes, you better solve the equations D[f[x,y],x]==0, D[f[x,y],y]==0 than doing a lengthy numerical proceedure. If your really need to do a minimize of maximize numerically, you can do this, but convergence is slow. Here is an example where you can watch the slow convergence: f[x_?NumericQ, y_?NumericQ] = (x^2 + y^2) + 2 Exp[-10 (x - .25)^2]; f1[y_?NumericQ] := (PrintTemporary[y]; NMaximize[{f[x, y], -.5 < x < .5}, x][[1]]) ContourPlot[f[x, y], {x, -1, 1}, {y, -1, 1}, ContourLabels -> True, Contours -> 20] NMinimize[{f1[y], -.5 < y < .5}, y, PrecisionGoal -> 2] the answer is: {2.06579, {y -> -3.35259*10^-10}} hope this helps, Daniel amber wrote: > There is a function f(x, y). > I need to find the minimum among the maximum of fixed y. > Namely: > g(x, y) = max_{B1<=x<=B2} f(x,y) > I need to get min_{A1<=y<=A2} g(x, y) > > But... > g[x_,y_] := First[Maximize[{f[x,y], B1<=x<=B2},x]]; > Minimize[{g[x,y], A1<=y<=A2},y] > > It doesn't work. How can I do? > > > >