Non linear optimization using MATLAB

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?

Answer 1

[Brendan Hamm]

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?

[Naseer Khan]

Thanks a lot for answering...and taking care.

[Brendan Hamm]

It is probably worth noting that your first 2 constraints are linear and can therefore be posed with the form Ax <= b.

Finally the last constraint is a bound and should be implemented as such.

Implementing linear constraints and bounds as non-linear constraints is generally inefficient.

[Naseer Khan]

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.

paper

[Naseer Khan]

@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]

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.