Gradient optimization problem with fmincon

2021 5 19
1 个回答
更新时间：2021 5 20
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0 个投票

Hi I'm currently working on an optimzation problem where I need to optimization a design dimension to minimize the ROI with Sequential Quadratic Programing with fmincon. However, I don't really know how the fmincon work and how my constrain will need to implement into the code. I'm new to matlab
Thank you for your time,
Here is my equation and constrain that I want to put in Matlab
with r is the radius and l is the length of the tank

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Dai Nguyen
Dai Nguyen 2021-5-19
ROI is the function that I want to minimize using fmincon
Torsten
Torsten 2021-5-19
What are you trying to minimize ?
Your ROI is constant and equals -0.95.
Dai Nguyen
Dai Nguyen 2021-5-19
I tried to minimize the ROI
Dai Nguyen
Dai Nguyen 2021-5-19
ROI depends on radius and length
I found the constraint between them and other requirements constraints. I just don't know how to do fmincon and how to put those constraint. Please help
Here are your variables are r and l. What constraints (in a range of numbers) do you have for r (radius) and l (length)?
Torsten
Torsten 2021-5-19
Your ROI doesn't depend on l and r.
It's constant and equals -0.95.
Dai Nguyen
Dai Nguyen 2021-5-19
Can you explain me why it doesn't depend on it cuz the volume change in the response of r and l. If r and l change the ROI needs to be changed also. how do you get -0.95 from it
Dai Nguyen
Dai Nguyen 2021-5-19
these are the constrainst
Dai Nguyen
Dai Nguyen 2021-5-19
This is the volume function
Dai Nguyen
Dai Nguyen 2021-5-19
my initial design is 5000 for length and 500 for radius
Dai Nguyen
Dai Nguyen 2021-5-19
yeah you are right it doesn't depends. I think in this case imma minimize the volume

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回答（1 个）

0 个投票

Here is a simple solution to your exercise. Adjust your constrains for r (radius) and l (length).
% NOTE: RL(1) is R and RL(2) is L.
ROI =@(RL) (.05*(509.7*pi(RL(1)^3+RL(1)^2*RL(2))+5.505e3*RL(1)^2)-509.7*pi*(RL(1)^3+RL(1)^2*RL(2))+5.505e3*RL(1)^2)/(509.7*pi*(RL(1)^3+RL(1)^2*RL(2))+5.505e3*RL(1)^3);
Rb = [0,0];
% NOTE: 0<=R<=5; 0<=L<=15; Thus, Rb= [0, 0]; and Lb = [5, 15];
Lb = [5, 15];
% No Other constraints are considered here
A = [];
b = [];
Aeq = [];
beq = [];
x0 = (Lb + Rb)/2;
RL = fmincon(ROI,x0,A,b,Aeq,beq,Lb,Rb);
R = RL(1);
L = RL(2);
fprintf('Found values: R = %f [ft] L = %f [ft] \n', [R, L])
Good luck.

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Dai Nguyen
Dai Nguyen 2021-5-19
can you explain for me what is Lb and Rb
Dai Nguyen
Dai Nguyen 2021-5-19
what is @RL is it the first derivative in term of r and l
RL is the variable: RL = [r, l];
Sulaymon Eshkabilov
编辑：Sulaymon Eshkabilov 2021-5-19
Now you have edited your problem statement significantly from the initially posted one. That means your function for minimization would be V(r, l) in the proposed code of mine.
And the constrains for r and l need to be inserted properly.
Dai Nguyen
Dai Nguyen 2021-5-19
ok do I need to delete the x0 ( it's the midpoint, isn't it)
That is an initial guess value. The search starts w.r.t x0 values. Good luck with your sims.
Dai Nguyen
Dai Nguyen 2021-5-19
Yeah I tried to put the constraints but my constraints is non linear
c(1)= L + R - 131.23; % height of tank
c(2) = 1224.303*RL(1)^2; % height of distance, fuel needed
c(3) = (RL(1)*RL(2))/(2*(RL(2)+RL(1)))- 0.25; % thickness of tank
Torsten
Torsten 2021-5-20
编辑：Torsten 2021-5-20
The first constraint is linear, the second is superfluous and the third can be put in function "nonlcon".
Read the documentation of fmincon for more details.

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Dai Nguyen
Dai Nguyen
2021-5-19

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Torsten
Torsten
2021-5-20

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