Re: NMinimize problem: fct minimized uses FindRoot
- To: mathgroup at smc.vnet.net
- Subject: [mg123552] Re: NMinimize problem: fct minimized uses FindRoot
- From: DrMajorBob <btreat1 at austin.rr.com>
- Date: Sun, 11 Dec 2011 03:45:56 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <201112101227.HAA19219@smc.vnet.net>
- Reply-to: drmajorbob at yahoo.com
1) Never, ever, EVER use Return. In this case, there wasn't even a flimsy excuse for it. 2) To prevent computing a function with symbolic arguments, use a pattern on the LHS such as _?NumericQ. 3) You used invalid syntax in the second argument of NMinimize. 4) Use Set, not SetDelayed, whenever possible. Clear[numFct] numFct[optvar_?NumericQ] := Module[{inteq, n, x}, inteq[x_] = (Sin[x] + 1/2*Cos[x])/optvar; Sin[optvar] + n /. FindRoot[inteq[n], {n, 0.1}]] NMinimize[numFct[var], {var, 0, 6}] {-1.46365, {var -> 4.71239}} 5) Finding a root for (Sin[x] + 1/2*Cos[x])/optvar is the same as finding a root for Sin[x] + 1/2*Cos[x]: Clear[numFct] numFct[optvar_?NumericQ] := Module[{inteq, n, x}, inteq[x_] = Sin[x] + 1/2*Cos[x]; Sin[optvar] + n /. FindRoot[inteq[n], {n, 0.1}]] NMinimize[numFct[var], {var, 0, 6}] {-1.46365, {var -> 4.71239}} 6) Don't define functions you don't need: Clear[numFct] numFct[optvar_?NumericQ] := Module[{x}, Sin[optvar] + x /. FindRoot[Sin[x] + Cos[x]/2, {x, 0.1}]] NMinimize[numFct[var], {var, 0, 6}] {-1.46365, {var -> 4.71239}} 7) Optimization and root-finding are uncoupled in this case, so: Clear[numFct] numFct[optvar_?NumericQ] := Sin[optvar] + Module[{x}, x /. FindRoot[Sin[x] + Cos[x]/2, {x, 0.1}]] NMinimize[numFct[var], {var, 0, 6}] {-1.46365, {var -> 4.71239}} or Clear[numFct, x, y] numFct[x_?NumericQ] = Sin[x] + y /. FindRoot[Sin[y] + Cos[y]/2, {y, 0.1}]; NMinimize[numFct[x], {x, 0, 6}] {-1.46365, {x -> 4.71239}} or even simpler: Clear[x] NMinimize[Sin[x], {x, 0, 6}] First@% + x /. FindRoot[Sin[x] + Cos[x]/2, {x, 0.1}] {-1., {x -> 4.71239}} -1.46365 Bobby On Sat, 10 Dec 2011 06:27:05 -0600, Doug Tinkham <dtinkham at live.ca> wrote: > Hello > > I'm using NMinimize and FindMinimum to minimize a function that uses > FindRoot when calculating it's value. The problem is that the equation > that FindRoot is used on uses the variable that is being optimized, and > Mathematica appears to be forcing the variable that is being optimized > to remain symbolic in the FindRoot call, and this leads to recursion and > a recursion limit error. > > Rather than post my actual functions that are quite long, I've reduced > my problem to the code below that shows my issue. As you will see, > FindRoot keeps optvar in symbolic form when executing FindRoot. Is there > a way to force Mathematica to use all numerical calculations using > NMinimize or FindMinimum? Is the issue with calculation of the > gradient, which Mathematica wants to do symbolically? > > Many thanks. > > > > MyNumFct[optvar_] := Module[{inteq, n}, > inteq[x_] := (Sin[x] + 1/2*Cos[x])/optvar; > n = n /. FindRoot[inteq[n], {n, 0.1}]; > Return[n + Sin[optvar]]; > ] > NMinimize[{MyNumFct[var], 0 <= var <= 6}, {var, 4.1}] > > -- DrMajorBob at yahoo.com
- References:
- NMinimize problem: fct minimized uses FindRoot
- From: "Doug Tinkham" <dtinkham@live.ca>
- NMinimize problem: fct minimized uses FindRoot