Re: Re: Problem with Maximize and conditions.

*To*: mathgroup at smc.vnet.net*Subject*: [mg51117] Re: [mg51101] Re: Problem with Maximize and conditions.*From*: DrBob <drbob at bigfoot.com>*Date*: Tue, 5 Oct 2004 04:37:03 -0400 (EDT)*References*: <200410020719.DAA26394@smc.vnet.net> <cjoj5g$ap6$1@smc.vnet.net> <200410041018.GAA25229@smc.vnet.net>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

> But it seems you're using brute force. It is nice to see how to use > brute force when all the other methods works. The other methods DON'T work. NMinimize, for instance, can't be trusted to return a feasible answer or warn you if it failed, and it may tell you it failed when it actually succeeded. The two fastest solutions I've seen so far are these: Timing[feasible = Select[ Flatten[Outer[List, Range[98], Range[98]], 1] /. {x_, z_} -> {x, 100 - x/20 - 5*z, z}, 1 <= #1[[2]] <= 98 && #1[[2]] \[Element] Integers & ]; ({Tr[#1], #1} & )[ First[feasible[[Ordering[ feasible, -1, Tr[#1] > Tr[#2] & ]]]]]] {0.062 Second, {43, {20, 4, 19}}} Timing[ a = Reduce[{(1/20)*x + y + 5*z == 100, x \[Element] Integers, y \[Element] Integers, z \[Element] Integers, 0 < x < 99, 0 < y < 99, 0 < z < 99}, {x, y, z}]; b = {ToRules[a]}; b[[First[Ordering[x + y + z /. b, 1]]]]] {0. Second, {x -> 20, y -> 4, z -> 19}} The first varies x and z in a brute force manner. The second starts with Reduce to enumerate the entire feasible space and ends with a brute force search for the smallest objective function value. Bobby On Mon, 4 Oct 2004 06:18:33 -0400 (EDT), Nacho <ncc1701zzz at hotmail.com> wrote: > Hello Dr.Bob. > > I don't understand very well all thoise # and @ yet ;) I'm on it... > > But it seems you're using brute force. It is nice to see how to use > brute force when all the other methods works. > > > Thanks for your solution. > > Best regards. > > DrBob <drbob at bigfoot.com> wrote in message news:<cjoj5g$ap6$1 at smc.vnet.net>... >> Minimize and NMinimize apparently can't solve this simple Integer problem; I'm sure somebody will explain to you why this is a good thing, but I can't. >> >> Meanwhile, here's an answer the hard way: >> >> Timing[feasible = Select[Flatten[ >> Outer[List, Range@98, Range@98, Range@98], 2], {1/20, 1, 5}.# == 100 &]; >> {Tr@#, #} &@First@feasible[[Ordering[feasible, -1, Tr@#1 > Tr@#2 &]]]] >> >> {9.687 Second,{43,{20,4,19}}} >> >> and here's a much faster solution: >> >> Timing[feasible = Select[ >> Flatten[Outer[List, Range[98], >> Range[98]], 1] /. >> {x_, z_} -> {x, 100 - x/20 - >> 5*z, z}, >> 1 <= #1[[2]] <= 98 && >> #1[[2]] \[Element] Integers & ]; >> ({Tr[#1], #1} & )[ >> First[feasible[[Ordering[ >> feasible, -1, >> Tr[#1] > Tr[#2] & ]]]]]] >> >> {0.078 Second, {43, {20, 4, 19}}} >> >> Bobby >> >> On Sat, 2 Oct 2004 03:19:15 -0400 (EDT), Nacho <ncc1701zzz at hotmail.com> wrote: >> >> > Hello. >> > >> > I was trying to solve a problem with Mathematica 5 and I am getting >> > strange results. >> > >> > The problem is: >> > >> > Minimize x+y+z, with the condition that 1/20x+y+5z==100 and x,y,z are >> > Integers between 1 and 98 (inclusive). >> > >> > So I use: >> > >> > Minimize[{x+y+z, 1/20 x+y+5z\[Equal]100, x \[Element] Integers, >> > y \[Element] Integers, z\[Element]Integers, 0<x<99,0<y<99,0<z<99}, >> > {x,y, >> > z}] >> > >> > I have copied the text using "Plain text" option, I hope it's fine. >> > >> > This returns the same expression, I suppose that Mathematica cannot >> > resolve it. So I use NMinimize: >> > >> > NMinimize[{x+y+z, 1/20 x+y+5z\[Equal]100, x \[Element] Integers, >> > y \[Element] Integers, z\[Element]Integers, 0<x<99,0<y<99,0<z<99}, >> > {x,y, >> > z}] >> > >> > Now I get a result, but rather weird... >> > >> > \!\({25.`, {x -> 1, y -> 5, z -> 1899\/100}}\) >> > >> > The minimum of x+y+z is 25 but z is 1899/100 >> > 1899/100 is not a Integers, and the nearest Integer, 19, doesn't >> > satisfy 1/20x+y+5z==100, and also x+y+z is not 25 but 24.99 >> > >> > I don't know why Mathematica has returned a Real when I specified an >> > Integers. I suppose that it is related to the use of NMinimize. I >> > suppose that it considers that 18.99 is so near of 19 that it can be >> > considered an Integer. >> > >> > If you remove the condition of z being an Integer, the result changes, >> > so it is affecting. Also, if you ask for "1899/100 e Integers" it >> > returns False. >> > >> > So, does anybody know how to solve this? Ideally, I would like to know >> > why Minimize doesn't work (so I have to use NMinimize), but in any >> > case, how to solve the problem. >> > >> > Thanks! >> > >> > >> > >> > > > > > -- DrBob at bigfoot.com www.eclecticdreams.net

**References**:**Problem with Maximize and conditions.***From:*ncc1701zzz@hotmail.com (Nacho)

**Re: Problem with Maximize and conditions.***From:*ncc1701zzz@hotmail.com (Nacho)

**Re: Problem with Maximize and conditions.**

**Re: A way around the limitations of Re[] and Im[]**

**Re: Problem with Maximize and conditions.**

**Problem with Maximize and conditions.**