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Non linear optimization using MATLAB

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Naseer Khan
Naseer Khan on 29 Dec 2017
Commented: Brendan Hamm on 3 Jan 2018
I have following question on Non linear optimization that came to my lab exam. I am trying to solve it but it is giving wrong answer.
Following is my objfun.m
function f = objfun(x)
f = 0.6224*x(1)*x(3)*x(4)+(1.7781*x(2)^2.0)*x(3)+(3.1661*x(1)^2.0)*x(4)+(19.84*x(1)^2.0)*x(3);
end
Following is my confun.m
function [c, ceq] = confun(x)
%Nonlinear inequality constraints
c = 1296000-(4/3)*pi*(x(3)^3.0)-pi*(x(3)^2.0)*x(4);
% Nonlinear equality constraints
ceq = [];
Following is my main file that calls both files
LB=[10,10,0.0625,0.0625];
UB=[200,200,6.1875,6.1875];
A=[-1,0,0.0193,0;0,-1,0.00954,0;0,0,0,1];
b=[0,0,240];
Aeq=[];
beq=[];
x0 = [0.5,0.5,10.221,11.334]; % Make a starting guess at the solution
%options = optimoptions(@fmincon,'Algorithm','sqp');
[x,fval] = fmincon(@objfun,x0,A,b,Aeq,beq,LB,UB,@confun,options);
My Solution
10.0000 10.0000 6.1875 6.1875
My solution is nowhere nearer to the given answer and the issue lies in initial guess?
On stackoverflow when I put this question which I have now deleted somebody commented that there is typo in question and constraints on x1,x2 and x3,x4 are reversed. I too agree with that as the solution given in position x3 and x4 have far greater values than the one allowed in the constraints.
But sill I am not being able to find the solution?

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Answers (1)

Brendan Hamm
Brendan Hamm on 29 Dec 2017
There is clearly an issue with the question as the provided solution does not provide a valid answer to the problem. That being said, the solution that was provided with the question is not correct and you cannot expect to get that answer. I would raise the question with your professor so that hopefully they can correct the issue. Maybe the objective function is also not correct?

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Naseer Khan
Naseer Khan on 30 Dec 2017
Sir can you change that thing in my MATLAB code? Also today I got a paper that has this problem in Section 2.4. I again checked that and it is same as I posted here.
Naseer Khan
Naseer Khan on 30 Dec 2017
@Brendan Hamm I have made changes as you suggested but still my solution is far far away. I guess my bounds are not ok and so is not my initial guess.
Brendan Hamm
Brendan Hamm on 3 Jan 2018
As I mentioned before, the solution provided does not satisfy the constraints, so there is little one can do to figure out the problem.
Also, if you wish to put files on here, upload them directly Using the Attach button. I will not follow links to other locations.

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