Items tagged with maximizemaximize Tagged Items Feed

Error when using maximize...

February 27 2016
0 3

When I put maximize(cos(t)), everything is fine.

When I put maximize(cos(Pi)), everything is fine.

When I put maximize(cos(t*Pi)), it says invalid limiting point??? What went wrong?

How to find maximum?...

February 18 2016
2 6

Hi all,

I have a function f(x) and want to know at which x-value it attains its supremum.

Tried this, but it doesn't work (or at least hasn't been able to solve the equation in 10+ min):

M := maximize(f, x = 0 .. 1);

solve(f = M, x);

Does anyone know a way to do this?

Thanks,

Paul

 (1)

 (2)

Help with optimization...

December 07 2015
0 6

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:

Maximize with numerical integrals...

July 23 2015
0 5

I am not sure how/why, but here is the worksheet.

test.mw

The function evalutes fine and can be used for sequence. But it does not seem to be working with plot or Maximize.

V is assumed to between 0 and 1.

Need some help.

Thanks,

casper

Substract location in the maximum of a function...

July 14 2015
1 8

Hi,

I have the following input

f:=x^2*exp(-1.2*x);
maximize(f, x=0..100,location);

Maple gives me the location is x=1.25. However, how should I do to obtain this position?  If I write

a:=maximize(f, x=0..100,location);

Seems it do not work :(

I may try fsolve at the maximum value, but it seems to be awkward..

Thank you very much!

Maximizing a function...

January 13 2015
0 5

Hi there,

I am trying to maximize a function given a set of values to a parameter in the function. The function is an differential equation belonging to a system of two differential equations.

I have a for loop to state different values to the parameter.

Maple yields the error:

Error, (in Optimization:-NLPSolve) cannot evaluate the solution further right of 0.17757507e-4, probably a singularity

When trying to maximize the function.

Supposed that I was doing something wrong in the loop, if I reproduce the contents of the loop outside, and set a value for the parameter. If I plot the solution of the ordinary differential equation, I can see where the maximum lies.

Having plot it, the Optimizamtion:-Maximize works as expected.

However, omitting the plot has a weird effect: I only get the same result depending on the bounds I set for the Maximization:

de1 := diff(A(t), t) = r*m*(1-g)*A(t)-piecewise(t < 8, r*A(t), t >= 8, (r+k)*A(t));
de2 := diff(G(t), t) = r*m*g*A(t)-l*G(t);

ics := A(0) = 25.0, G(0) = 0.;
num := dsolve({de1, de2, ics}, {A(t), G(t)}, type = numeric, output = listprocedure, parameters = [g]);

num(parameters = [g = .15]);
val := eval(G(t), num);

# odeplot(val, [t, G(t)], t = 0 .. 100);

Maximize(val);
Error, (in Optimization:-NLPSolve) cannot evaluate the solution further right of 0.17757507e-4, probably a singularity

val2 := Maximize(val);

Error, (in Optimization:-NLPSolve) cannot evaluate the solution further right of 0.17757507e-4, probably a singularity

val3 := Maximize(val(t), t = 0 .. 60);

[10267.824035766165, [t = 8.25727747134303]]

val4 := Maximize(val(t), t = 0 .. 100);

[6.863211343195069e-9, [t = 59.84184367042171]]

The right answer is [10267.824035766165, [t = 8.25727747134303]]: Why do I get two different answers even if in that range there is only one relative maximum?

I ignore whether the way I am specifying the arguments for the Maximize function is correct. val is a procedure.

What am I missing?

Attached is the worksheet: MaplePrimes_malaria_param_variation_2.mw

Thanks,

jon

the maximize of equation...

December 18 2014
0 6

I want to solve maximize of equation,but the maximize failed to solve it,who can help me.thanks.

 (1)

 (2)

 (3)

 (4)

 (5)

 (6)

Iwant to maximize the equation (5)and (6),under the conditon of x,y,z are negative or positive at the same time.

How can I find the greatest value of this expressi...

September 12 2014
1 15

I want to find the greatest value of this expression

f:=(x,y,z)->sqrt((x+1)*(y^2+2)*(z^3+3))+sqrt((y+1)*(z^2+2)*(x^3+3))+sqrt((z+1)*(x^2+2)*(y^3+3));

with x>0, y>0 , z>0,x+y+z=3.

I tried

restart:

f:=(x,y,z)->sqrt((x+1)*(y^2+2)*(z^3+3))+sqrt((y+1)*(z^2+2)*(x^3+3))+sqrt((z+1)*(x^2+2)*(y^3+3));

DirectSearch[GlobalOptima](f(x,y,z), {x>0, y>0 , z>0,x+y+z=3},maximize);

I got the output

[HFloat(infinity), [x = .591166078050740e52, y = .183647204560715e52, z = .786638021216969e52], 1249]

How do I do optimization...

July 18 2014
0 1

Hi all

I am trying to maximize a function f(x,y,z,w) in terms of x. (Only x is treated as a variable, and the others are treated as parameters).

However, all I know is that y,z,w they are parameters and they are non-negative. I have already tried with the "optmization help page" from maplesoft's website, and it looks like it will search the range of x,y,z,w, and it will return numerical values at which this function is maximized.

However, what I want is instead a close-form solution of x=g(y,z,w) that will maximize the function.   In other words, I would like to keep the parameter in symbolic forms.

Can Maple do that?

Maple and Matlab - Global Optimization toolbox...

July 17 2014
1 23

Hi,

On page 32 （PDF）

Two different results were obtained using the Global optimization.

Log likelihood does not differ much. BUT the estimates vary a lot, such as mu[p].

tmp.mw

tmp.pdf

When I tried to use one of the answer from a particular run, I get the HFLOATING error, see picture.

So how reliable is this? Could there be a better way to optimize this ?

Thanks!

As an additional note, if I have Matlab R2014a, could I use Matlab to optimize the target function? DO I need to purchase a seperate addon?

Optimization [Minimize] and [Maximize] with Pi...

April 20 2014
2 3

what is the wrong with Pi set ::: in this function ::: Warning, no iterations performed as initial point satisfies first-order conditions

Optimization[Minimize](x^2 + y^2 + 25*(sin(x)^2+sin(y)^2), x=-2*Pi .. 2*Pi , y= -2*Pi .. 2*Pi);

Warning, no iterations performed as initial point satisfies first-order conditions
[0., [x = HFloat(0.0), y = HFloat(0.0)]]

Optimization[Maximize](x^2 + y^2 + 25*(sin(x)^2+sin(y)^2), x=-2*Pi .. 2*Pi , y= -2*Pi .. 2*Pi);

Warning, no iterations performed as initial point satisfies first-order conditions
[-0., [x = HFloat(0.0), y = HFloat(0.0)]]

--------------------------------

I got my good result when I apply it with this function :

f:= (x,y)->cos(x)*sin(y) -(x/(y^2+1));

Optimization[Maximize](f(x,y), x = -1 .. 2, y = -1 .. 1);

[0.994945017202501170,[x = HFloat(-0.6362676080636113), y = HFloat(1.0)]]

Optimization[Minimize](f(x,y), x = -1 .. 2, y = -1 .. 1);

[-2.02180678335978703,[x = HFloat(2.0), y = HFloat(0.10578346945175972)]]

Optimization of multivariate functions with inequa...

March 28 2014
1 1

I need to maximize two multivariate objective functions (f(x1,y1,z1,t1) and g(x2,y2,z2,t2)) with inequality and nonnegativity constraints (x1, x2>0 and y1, z1, t1, y2, z2, t2 >=0). I am looking for parametric not numerical solutions.

What is the best way to find the solution to such a problem using maple?

Error, (in Optimization:-NLPSolve) complex value ...

March 22 2014
0 1

When using Maximize, is it possible to now what parameter settings that resulted in complex numbers?

KR Fredrik

Maximize(Eq1_new, {R_K*rho*`&sigma;_K`+R_S*`&sigma;_S` >= .38780613588076011954, r_K*rho*`&sigma;_K`+r_S*`&sigma;_S` >= .21290471165685214846, R_K*rho*`&sigma;_K`+R_S*`&sigma;_S` <= .38780613588076011954, r_K*rho*`&sigma;_K`+r_S*`&sigma;_S` <= .21290471165685214846});

Error, (in Optimization:-NLPSolve) complex value encountered

Maple maximize doesn't execute...

January 27 2014
2 4

Hello everyone,

Jus started using Maple and I was wondering why maple doesn't execute the following function:

Thx,

Frank

maximum & minimum of aN implicit function...

December 07 2013
0 8

Hi every one,

Q1:

I tried to get the max \$ min of a following function:

l:=1:alpha:=1:b:=100:k:=20:

eq1 := (alpha+(l+alpha)*u+alpha*k*u^2)*a =
u*(alpha+(l+alpha)*u+alpha*k*u^2)*(1+l*alpha*b/((alpha+(l+alpha)*u+alpha*k*u^2))):

I did this code but it seems it didnt work for this equation

maximize(eq, u=1..12, location);

minimize(eq, u=1..12, location);

Also, I think about solving the cubic i feel i'm so close to the solve but couldn't

factor((rhs-lhs)(eq1));

eq:=collect(%,u);

Q:=(a,u)->eq;sol:=evalf(solve(Q(a,u),u)): S:=array([],1..3): S[1]:=sol[1]:S[2]:=sol[2]:S[3]:=sol[3]:

Q2:

the same thing wanted to get the maximum and the minimum of the function v

here the code

restart;
eq1:=(alpha+(l+alpha)*u+alpha*k*u^2)*a=
u*(alpha+(l+alpha)*u+alpha*k*u^2)*(1+l*alpha*b/((alpha+(l+alpha)*u+alpha*k*u^2)));
eq2:=v=alpha*b*(1+u+k*u^2)/(alpha+(l+alpha)*u+alpha*k*u^2);
factor((rhs-lhs)(eq1));
eq1:=collect(%,u);
params:={l=10,alpha=0.5,b=100,k=20};
U:=[solve(eval(eq1,params),u)]; #3 solutions for u
#plots:-complexplot(U,a=0..20,style=point); #plot in the complex u-plane
vua:=eval(solve(eq2,v),params): #v expressed in terms of u and a
V:=eval~(vua,u=~U): #the 3 solutions for v in terms of a

## PLOT the function V
plot(V,a=0..75,v=0..100,color=black,labels=[a,v],axes=boxed,numpoints=90,linestyle=1,font=[1,1,18],thickness=2,tickmarks=[4,4],view=[0..65,25..100]);

I do appricaited any advises

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