How to optimize parameters that satisfy the equation.

I want to optimize three parameters x, y, z that satisfy the following equation.

A(D) = abs(x * (y * exp(1i * z) * B(D) + C(D)))

A (D), B (D), C (D): Constant determined by D

i : imaginary unit

However, it does not converge to the expected value.

What sholud I do about this situation?

I used the Optimize Live Editor Task with the following contents by referring to the following URL.

https://www.mathworks.com/help/matlab/math/optimize-live-editor-matlab.html

Objective : Nonlinear

Constraints : Unconstrained

Solver : fminsearch

Objective function : Local function, objectiveFcn

Initial point : x0 = [3 2 pi]

This time, A (D) = 0.24, B (D) = 0.05, C (D) = 0.02, and the Local function is described as follows.

At this time, x, y, and z are expected to be 3, 2, pi, respectively.

---------------------------------------------------------

function f = objectiveFcn(optimInput)

x = optimInput(1);

y = optimInput(2);

z = optimInput(3);

f = 0.24 - abs(x*(0.05*y*exp(1i*z) + 0.02));

end

---------------------------------------------------------

Answer 1

[Matt J]

First, you must fix the formula for f

f = abs( 0.24 - abs(x*(0.05*y*exp(1i*z) + 0.02)) );

Second, you have 3 unknowns, so you must provide at least 3 equations.

[KM]

Thank you for your comments.

I fixed the formula.

And concerning 3 equations, in fact A(D), B(D) and C(D) are functions of D,

so it is possible to prepare over 3 equations. (For example, D=100, 200, 300)

In this case, how should the Local function be described?

[Matt J]

In the above f measures the violation of one equation. With more than one, you should sum the violations of all equations.

[KM]

I’m so sorry for taking so long to get back to you.

What does "sum the violations" mean?

I can't understand the meaning of this sentence,

so I don't know what I should do specifically.

I'm sorry to ask you so many questions.

[Matt J]

For example, if your equations were the 2x2 system A*x=b

A=rand(2); b=sum(A,2);

f=@(x) sum(abs(A*x-b));

x=fminsearch(f,[0;0])

x = 2×1

1.0000 1.0000

[KM]

Thank you for your quick reply.

It looks like I will optimize my equations by referring to your example.

Thank you so much again.