maximizing objective function with equality and inequality constraints

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Az.Sa 2023-1-20

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评论： Torsten 2023-6-23

采纳的回答： Aditya

Hi,

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

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Torsten 2023-1-20

编辑：Torsten 2023-1-23

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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采纳的回答

Aditya 2023-1-23

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编辑：Aditya 2023-1-23

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Hi,

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.

And what can i do if i want to use the linprog function in simulink and use it at every time step ? Because when i use it, it shows me an error that "the function 'linprog' is not supported for code generation."

Torsten 2023-6-23

I have no experience with this coupling, but this contribution might be helpful:

https://uk.mathworks.com/matlabcentral/answers/228714-linear-programming-using-simulink

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