solve non-linear optimization problem

2021 4 26
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更新时间：2021 4 28
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how to maximize this nonlinear function z and find the value of x and y,
z= 0.031 {0.009[exp⁡(x-z)-1]+x/1.14}-(-1+√(1+y^4/x))/y
10<=x<=20 and y>=0

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Matt J
Matt J 2021-4-26

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With fmincon, if you have Optimization Toolbox.
https://www.mathworks.com/help/optim/ug/fmincon.html

19 个评论
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Hayam Wahdan
Hayam Wahdan 2021-4-26
The main problem of this optimization problem, the objective function z is calculated in terms of the same value of z
Matt J
Matt J 2021-4-26
编辑：Matt J 2021-4-26
You "objective" is really an equality constraint:
Hayam Wahdan
Hayam Wahdan 2021-4-26
After this assumption, the problem contains three decision variables x,y and z?
Hayam Wahdan
Hayam Wahdan 2021-4-26
How fminco function solve this optimization problem
Min -Z
St
Z-....=0
d>=100
d<=300
v>=0
Matt J
Matt J 2021-4-26
Did you already get it to work on your original problem, and if so how is this new version different?
Hayam Wahdan
Hayam Wahdan 2021-4-26
I want to ask, can this function solve this optimization problem subject to non-linear constraints
Walter Roberson
Walter Roberson 2021-4-26
Yes, see the nonlcon parameter of fmincon.
Matt J
Matt J 2021-4-26
编辑：Matt J 2021-4-26
I want to ask, can this function solve this optimization problem subject to non-linear constraints
Yes, see this example in the documentation:
https://www.mathworks.com/help/optim/ug/fmincon.html#busow0u-1
Note that you don't really have to ensure that the initial guess satisfy the constraints, as they do in the example, but it can be beneficial to do so.
Hayam Wahdan
Hayam Wahdan 2021-4-27
Can you help me in writing this MATLAB function Min -Z St z= 0.031 {0.009[exp(x-z)-1]+x/1.14}-(-1+√(1+y^4/x))/y 10<=x<=20 and y>0
Walter Roberson
Walter Roberson 2021-4-28
编辑：Walter Roberson 2021-4-28
Ran in:
Ran in:
fmincon thinks you can get an arbitrarily large result if you make y arbitrarily large.
format long g
obj = @(xyz) -xyz(3);
A = []; b = []; Aeq = []; beq = [];
lb = [10, realmin, -inf];
ub = [20 1e9 1e9];
nl = @(x,y,z) 0.031*(0.009*(exp(x-z)-1)+x./1.14)-(-1+sqrt(1+y^4./x))./y - z
nl = function_handle with value:
@(x,y,z)0.031*(0.009*(exp(x-z)-1)+x./1.14)-(-1+sqrt(1+y^4./x))./y-z
nonlcon = @(xyz) deal(nl(xyz(1), xyz(2), xyz(3)), []);
xyz0 = [.1 .2 .3]
xyz0 = 1×3
0.1 0.2 0.3
[best, fval] = fmincon(obj, xyz0, A, b, Aeq, beq, lb, ub, nonlcon)
Local minimum found that satisfies the constraints. Optimization completed because the objective function is non-decreasing in feasible directions, to within the value of the optimality tolerance, and constraints are satisfied to within the value of the constraint tolerance.
best = 1×3
17.9264664551072 190469849.537475 999999999.999999
fval =
-999999999.999999
Walter Roberson
Walter Roberson 2021-4-28
Please re-check your equations. I suspect that the sqrt() is intended to extend over the /y as well, which is not what you have coded.
Hayam Wahdan
Hayam Wahdan 2021-4-28
Thank you very much for your quick reply,
when i tried this code, gave me error in this line
[best, fval] = fmincon(obj, v0, A, b, Aeq, beq, lb, ub, nonlcon)
Walter Roberson
Walter Roberson 2021-4-28
What was the error message?
Hayam Wahdan
Hayam Wahdan 2021-4-28
Error using barrier
Nonlinear constraint function is undefined at initial point. Fmincon cannot continue.
Error in fmincon (line 798)
[X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] = barrier(funfcn,X,A,B,Aeq,Beq,l,u,confcn,options.HessFcn, ...
Error in nonlinear (line 11)
[best, fval] = fmincon(obj, vdJ0, A, b, Aeq, beq, lb, ub, nonlcon)
Walter Roberson
Walter Roberson 2021-4-28
please post the complete code you used.
Hayam Wahdan
Hayam Wahdan 2021-4-28
编辑：Walter Roberson 2021-4-28
format long g
obj = @(xyz) -xyz(3);
A = []; b = []; Aeq = []; beq = [];
lb = [100, realmin, -inf];
ub = [300 1e9 1e9];
%nl = @(x,y,z) 0.031*(0.009*(exp(x-z)-1)+x./1.14)-(-1+sqrt(1+y^4./x))./y - z
w=10^-15*exp(-2.897*10^22*25^-1);
nl = @(x,y,z) 0.055*(w*(exp(5802*(x-19.5*z))-1)+x./1.14)-(-1+sqrt(1+0.5272*y^4./x^2.))/(2.6328 *10^9*y) - z;
nonlcon = @(xyz) deal(nl(xyz(1), xyz(2), xyz(3)), []);
xyz0 = [.1 .2 .3];
[best, fval] = fmincon(obj, xyz0, A, b, Aeq, beq, lb, ub, nonlcon)
Walter Roberson
Walter Roberson 2021-4-28
w=10^-15*exp(-2.897*10^22*25^-1);
You badly need to rescale !!
exp(-1158800000000000000000) is about
Effectively your w is 0.
Hayam Wahdan
Hayam Wahdan 2021-4-28
Thank you very much, I will rescale it

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