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I'm having trouble with using constrained optimization to solve a problem.

The problem is set up as:

Max: w=x1/2 y1/4

Subject to: K=x+4. K is a constant.


I'm not sure where to start.

I know how to use Maple for an optimization problem contaning continous variables but I couldn't find anything in help of Maple related to use boolean variables in optimization. So assume I want to minimize a function that one of its variables only can take 0 and 1 as its value. Anyone knows how to introduce those to the Maple? For example you can look at this link that Matlab can do many of these kind of optimizations.

Hi everybody i've to minimize a function of about 5-6 variables so i tried some of maple functions like: 'Minimize', 'minimize', 'NLPSolve' but with 'minimize' my pc goes in loop and it eats a lot of ram without giving some results, while with the Optimization package i got the error :'

Error, (in Optimization:-NLPSolve) abs is not differentiable at non-real arguments


code :


L := 1:
b := 1.1:
p := 1.8:
xa := 0:
xd := -b/2:
ya := -p+z:
yd := 0:

quadrilatero := proc(q,xa,ya,xd,yd,l1,l2,l3,modo,alpha0,alpha1)
local xb,yb,l5,c,alpha,theta5,theta2,xc,yc,theta3,xm,ym:

xb := xa+l1*cos(q + alpha0 + pi/2):
yb := ya+l1*sin(q + alpha0 + pi/2):
l5 := sqrt((xd-xb)^2+(yd-yb)^2):
c := (l2^2+l5^2-l3^2)/(2*l2*l5):
if modo = 1 then alpha := arccos(c) else alpha := -arccos(c) end if:
theta5 := arctan(yd-yb,xd-xb):
theta2 := theta5 + alpha:
xc := xb + l2*cos(theta2 + pi):
yc := yb + l2*sin(theta2 + pi):
theta3 := arctan(yd-yc,xd-xc):
return (theta3 - pi - alpha1):
end proc:
#funione sterzo
f := proc(q,ya,l1,l2,l3,yd,alpha0,alpha1)
local theta;
theta := quadrilatero(q, 0, ya,-b/2,0, l1, l2, l3, -1,alpha0,alpha1) - pi/2;
if theta < Pi and Im(theta) = 0 then theta := theta + 2*pi end if;
return theta;
end proc:
#funzione desiderata
Yd(q) := arctan(tan(q),(1 - b*tan(q)/2/p));
arctan(tan(q), 1 - 0.3055555556 tan(q))

#Definisco procedura dei minimi quadrati:
n := 1: i := 0:
q := Vector[n]: rms := 0:
for i from 0 by 1 to (n-1) do
q[i] := Pi*(i/(4*n)):
rms := rms + abs(f(q[i],ya,l1,l2,l3,yd,alpha0,alpha1) - yd(q[i])^2):
end do:
rms := sqrt(rms / n):
#MIN := (minimize(rms, z = -0.4..0,alpha0 = 0..Pi/3,alpha1 = Pi/2..5*Pi/4,l1 = 0.3..1,l2 = 0.001..0.3,l3 = 0.01..0.3,iterationlimit = 100));
Error, (in Optimization:-NLPSolve) abs is not differentiable at non-real arguments


thanks in advance for your help !


When I use the option assume = nonnegint or integervariables = {...} in Optimization[Minimize], or Optimization[LPSolve] I've got the message "kernel connection lost'. 


Thie even happens when I use the simple example from the Maple help:



It says; mserver.exe has stopped working. 

What's wrong? 

I've got this huge chunk of code which leads to an optimiazation at the very last line (Bestangles:=minimize(maximize()-minimize))). This minization is taking a very long time (havent solved it yet) and I would very much like to reduce that time. As I've understood maple does optimization by differentiating and then finding all extremes and comparing. Would this mean that since I minimize and optimize within a minimization command, it differentiates a ton of times? And if this is the case, can I somehow do the differentiation beforehand, since it is the same function being differentiate all the time? Or is there some other way I can improve the code? 
Thanks alot!

Heres the full code:


I would like to know how to do the following. If I received a plot of a graph, but I did not know it function, how could I get an accurate value for its maximum and minum points? Any help is greatly appreciated! Thank you in advance!

Kind regards,

Gambia Man


how to solve lp  on maple when consrtaints are in interval 



 i try to find this on maple,but i could not found my desired ans.

i got an assignment in which 15 constraints are given and all are in interval.

anyone know the ans then plz help me

Hi all,

I have been trying to plot Riemann Zeta Function on certain range, but it takes a lot of time(several minutes ,maybe hours).These are the basic things.

How to speed up ploting Zeta?

The same problem with Optimization.

Mathematica don't have this such problems.

Mathematica ploting Zeta with 0.125 second and optimizing 3.42 second.Maple few hours maybe......





I ues the optimization tool in Maple2015.

In my experience, Maple optimizatiom tool just shows the optimum values, not a history of the optimizatiom process.

I want to know how I can obtain the history of the optimization process, such as values of the objective, constraints, and tolerance at every iteration.

Is there anyone who knows how to obtain the history data of the optimization process?


Hi, i got a litlle problem with fromats, i m realy bad at this.
i got procedure 'getone(z::list)' i was execute it like this  
>getone([seq(lineP[i], i = 1 .. pm)]::list)
where lineP is 

>pm := 3;
>rollx := rand(98.0 .. 102.0); rolly := rand(-1.0 .. 5);
>rolll := rand(.5 .. 1.0); rollf := rand(0. .. evalf(2*Pi));
>rollm := rand(0. .. 20.0);

>for i to pm do lineP[i] := [rollx(), rolly(), rolll(), rollf(), rollm()] end do;

it's pm times of z:=[rollx(), rolly(), rolll(), rollf(), rollm()] ::list

and i need make optimization work for any pm=1..100; with rabdomly generated iteration point as above.

The main queston is how make minimize as below
Minimize(z,variables=[z],   initialpoint={z=[seq(lineP[i], i = 1 .. pm)]},iterationlimit=1000,optimalitytolerance=0.01)

work with z::list kind of 

[[100.7798614, 1.109653266, 0.9840371500, 4.257816686, 9.737110573][100.0135459, 0.887539481, 0.9144164697, 3.980093624, 7.343851161][100.0661308, 3.724268229, 0.5020544909, 2.052134822, 14.37408543]]


Portfolio Optimization with Google Spreadsheet and Maple

I will in this post show how to manage data and do portfolio optimization in Maple by using google spreadsheet.

You can either use a direct link to the data:

or you can set up your own google spreadsheet. If you choice to set up your own spreedsheet follow the below road map:

1) select which market you want to follow:




2) Create a new google spreadsheet and name two sheets Blad1 and Panel. In the first cell of Blad1 you put the formula:


you need to change the url to match your selection in 1).

3) In the first cell of Panel you put the name "Ticker" and then you copy all the ticker names from Blad1.

4) In the script editor you put in the below java script code:

function PanelCreation_Stock() 

var ss = SpreadsheetApp.getActiveSpreadsheet();
var sourceSheet = ss.getSheetByName("Blad1");
var dstSheet = ss.getSheetByName("Panel");
var curDat = new Date();
var day1 = curDat.getDay();
if(day1 == 0 || day1 == 1)
var lCol = dstSheet.getLastColumn();
var srcdate = dstSheet.getRange(1, 1, 1, lCol).getValues();

for(var k=1;k<=srcdate[0].length-1;k++)
if(Utilities.formatDate(srcdate[0][k],"GMT", "dd-MMM-yy") == Utilities.formatDate(curDat,"GMT", "dd-MMM-yy"))
var snRows = sourceSheet.getLastRow();
var dnRows = dstSheet.getLastRow();

var srcStock = sourceSheet.getRange("A2:A" + snRows).getValues();
var srcLastSale = sourceSheet.getRange("C2:C" + snRows).getValues();

var dstStock = dstSheet.getRange("A2:A" + dnRows).getValues();
var dstLastSale = dstSheet.getRange("Z2:Z" + dnRows).getValues();

for(var j=0;j<dnRows-1;j++)
var flag = "true";
var foundStock;
for(var i=0;i<snRows-1;i++) //snRows
var sStockVal = srcStock[i][0];

//var foundStock = ArrayLib.indexOf(dstStock,0, sStockVal);

for(var j=0;j<dnRows-1;j++)
if(dstStock[j][0].toString().toUpperCase() == srcStock[i][0].toString().toUpperCase())
flag = "true";
foundStock = j;
dstLastSale[foundStock][0] = srcLastSale[i][0];
var dnRows1 = dstSheet.getLastRow()+1;
dstSheet.getRange("A" + dnRows1).setValue(srcStock[i][0]);
for(var k=2;k<=lCol;k++)
if(dstSheet.getRange(dnRows1, k).getValue()=="")
dstSheet.getRange(dnRows1, k).setValue("n/a");
dstSheet.getRange(2, lCol+1, dstLastSale.length, 1).setValues(dstLastSale);

5) Set it to run each day at 12:00. The code will save the new last sale price for monday to friday with one days lag.

Now we can move on to Maple.

In Maple run the following code to load the data:


X := proc (Url) local theDLL, URLDownloadToFile, myDirectory, myFile, Destination, DL;


theDLL := "C:\\WINDOWS\\SYSTEM32\\urlmon.dll";


URLDownloadToFile := define_external('URLDownloadToFileA', pCaller::(integer[4]), szURL::string, szFileName::string, dwReserved::(integer[4]), lpfnCB::(integer[4]), 'RETURN'::(integer[4]), LIB = theDLL);


if FileTools[Exists]("C:\\mydir") = true then FileTools:-RemoveDirectory("C:\\mydir", recurse = true, forceremove = true) else end if;


myDirectory := "C:\\mydir";
myFile := "data1.csv";
Destination := cat(myDirectory, "\\", myFile);


DL := proc () local M;


URLDownloadToFile(0, Url, Destination, 0, 0);
M := ImportMatrix("C:\\mydir\\data1.csv", delimiter = ",", datatype = string);
M := Matrix(M, datatype = anything)


end proc;


return DL()


end proc:


data := X("");
L := LinearAlgebra:-Transpose(data);

If you use your own spreadsheet you need to change the url to match that spreadsheet.
Select File -> Publish to the web in google spreadsheet

We can now run the portfolio optimization in Maple:



Nr, Nc := ArrayTools:-Size(L):
symb := L[1 .. 1, 2 .. Nc]:
LL := L[2 .. Nr, 2 .. Nc]:
Nr, Nc := ArrayTools:-Size(LL):


# Removing stocks with missing observations
for i to Nc do if Occurrences("n/a", convert(Column(LL, i), list)) >= 1 then AA[i] := i else AA[i] := 0 end if
end do;


DD := RemoveInRange([seq(AA[i], i = 1 .. Nc)], 0 .. 1):
symbb := DeleteColumn(symb, DD):
LLL := map(parse, DeleteColumn(LL, DD)):
Nr, Nc := ArrayTools:-Size(LLL):


# Calculate Return
for j to Nc do
for i from 2 to Nr do


r[i, j] := (LLL[i, j]-LLL[i-1, j])/LLL[i-1, j]


end do
end do;


RR := Matrix([seq([seq(r[i, j], j = 1 .. Nc)], i = 2 .. Nr)], datatype = float[8]);
n, nstock := ArrayTools:-Size(RR):


# Portfolio Optimization
W := Vector(nstock, symbol = w):
y := Vector(n, fill = 2, datatype = float[8]):
s1 := Optimization[LSSolve]([y, RR])[2];
Nr, Nc := ArrayTools:-Size(s1):


j := 0:
for i to Nr do if s1[i] <> 0 then j := j+1; ss1[j] := symbb[1, i] = s1[i] end if end do;


Vector(j, proc (i) options operator, arrow; ss1[i] end proc);




Hello everybody,

I am new on this forum, and please to join your community.
As part of a project related to Origami, I try to follow the paper entitled "Mathematical Approach to Model Foldable Conical Structures Using Conformal Mapping", in order to flat-fold a conical structure.

As described in the paper a non-linear system need to be solved in order to get a corrected angle beta... The paper advize the use of "fsolve" function in Matlab, but I did not manage to do it... So I tried with Maple, but I get an error using NLPSolve, and I do not understand why...

Here is the edited, withdrawn and finally back file :

Do not hesitate to ask for any other explanations.

Any help is going to be appreciated.


How to find the maximum natural number n s. t. the sum of its cubed digits is greater than or equal to n? Of course, with Maple. The same question for the sum of the  digits to k-th power. Here are my unsuccessful attempts:
1.Optimization:-Maximize(n, {n <= convert(map(c ->c^3, convert(n, base, 10)), `+`)}, assume = integer);

Error, invalid input: `convert/base` expects its 1st argument, n, to be of type {integer, list(integer)}, but received n

2. for n while n <= convert(map(c ->c^3, convert(n, base, 10)), `+`) do print(n) end do;


Hi all,

Hope all to be in good health.

I have written following program to obtain minimum  under som constraints but it doesn't work due to some unknown error.

can any one help me?



best wishes

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department

This problem has real world applicability: Three vampires and three maidens are at the foot of a tall building and wish to get to the bar on the top floor.  The lift only holds two people (for convenience I am classing vampires as people), and needs one person to operate it.  If ever the vampires outnumber the maidens at any place, they will do something unspeakable.  How can the vampires and maidens all safety get to the top in the minimum of moves?

can this be solved procedurally or using optimization package?

possible manual soln:

No. m>= No. v

3m+3v, 0   [0]

2m+2v,m+v [1]

3m+2v,v  [2]

     3m, 3v [3]

3m+v , 2v  [4]

m+v  , 2m+2v [5]

#then reverse the steps

2m+2v, m+v [6]

       2v, 3m+v [7]

       3v, 3m  [8]

        v , 3m+2v [9]

    m+v, 2m+2v [10]

        0, 3m+3v [11]


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