maximizing objective function with equality and inequality constraints

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I want to estimate x_1 ,...,x_4 by maximizing
subject to and ,
which function can help me to solve this problem ,
Also, how can I convert this objective function to be convex if that is possible.
Thanks in advance
  1 Comment
Torsten on 20 Jan 2023
Edited: Torsten on 23 Jan 2023
x1=x2=x3=0, x4=1
Should be obvious because the coefficient of x4 has the maximum value of all coefficients.
And your objective function is convex.

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Accepted Answer

Aditya on 23 Jan 2023
Edited: Aditya on 23 Jan 2023
I understand that you want to solve this linear programming problem.
The solution for your example is trivial, as pointed out by @Torsten in comments.
In general, you can also use the linprog function to solve such problems. Here is an example to arrive at the trivial solution for your example.
Based on the documentation of linprog, I have defined the variables:
f = [4.22117991, 4.21111679, 4.22994893, 4.23060394];
Aeq = [1, 1, 1, 1];
lb = [0, 0, 0, 0];
beq = [1];
x = linprog(-f, [], [], Aeq, beq, lb, []);
You can see that the variable x is [0;0;0;1] which is the trivial solution to this problem.
The reason why I have passed negative f ( -f ) is because linprog minimizes the objective function. So, in order to maximize f, we minimize -f.
Torsten on 3 Feb 2023
Yes, that makes sense.
And the solution is as simple as in the case for t=1.
Take the row with the maximum sum, say row i, and set the corresponding a(i) to 1 and all other a(j)'s to 0.

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