Gradient optimization problem with fmincon

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

[Dai Nguyen]

ROI is the function that I want to minimize using fmincon

[Torsten]

What are you trying to minimize ?

Your ROI is constant and equals -0.95.

[Dai Nguyen]

I tried to minimize the ROI

[Dai Nguyen]

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

[Sulaymon Eshkabilov]

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]

Your ROI doesn't depend on l and r.

It's constant and equals -0.95.

[Dai Nguyen]

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]

these are the constrainst

[Dai Nguyen]

This is the volume function

[Dai Nguyen]

my initial design is 5000 for length and 500 for radius

[Dai Nguyen]

yeah you are right it doesn't depends. I think in this case imma minimize the volume

Answer 1

[Sulaymon Eshkabilov]

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.

[Dai Nguyen]

can you explain for me what is Lb and Rb

[Dai Nguyen]

Thank you so much

[Dai Nguyen]

what is @RL is it the first derivative in term of r and l

[Sulaymon Eshkabilov]

RL is the variable: RL = [r, l];

[Sulaymon Eshkabilov]

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]

ok do I need to delete the x0 ( it's the midpoint, isn't it)

[Sulaymon Eshkabilov]

That is an initial guess value. The search starts w.r.t x0 values. Good luck with your sims.

[Dai Nguyen]

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]

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.