how to optimize a multivariable function in matlab in matlab

To optimize a multivariable function in MATLAB, we can use a gradient-based algorithm. One of the most common MATLAB functions for this purpose is fminunc. Here is an example code for optimization of a multivariable function:

main.m
% Define the multivariable function to optimize
f = @(x) x(1)^2 + x(2)^2;

% Initialize the starting point
x0 = [0,0];

% Call the optimization function
[x, fval] = fminunc(f, x0);

% Display the optimized output
disp(['Optimized value of x: ' num2str(x)]);
disp(['Optimized value of f(x): ' num2str(fval)]);
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In this example, we define a simple multivariable function f with two variables x(1) and x(2). We then initialize the starting point as x0 = [0,0]. The fminunc function is called with the f function and x0 as inputs. The function returns x, which is the optimized value of x, and fval, which is the optimized value of f(x). We then display the optimized output using the disp function.

Note that fminunc requires the function being optimized to return the objective value and the gradient value as separate outputs. If the gradient is not provided, the algorithm uses a finite difference approximation to obtain it. Therefore, it is recommended to supply the gradient to improve the optimization speed.