find the global minimum of x, y variables in 3d function in matlab

To find the global minimum of a function of two variables (x, y) in Matlab, you can use the "fmincon" function. Here's an example of how to use this function to minimize a 3D function:

main.m
% Define the function
syms x y
f = x^2 + y^2 + exp(-x^2-y^2);

% Convert the symbolic function to a MATLAB function
fmat = matlabFunction(f);

% Define the initial guess for the solution
x0 = [0,0];

% Define the bounds for the solution
lb = [-10,-10];
ub = [10,10];

% Define the options for the optimization algorithm
options = optimoptions('fmincon','Display','iter','Algorithm','sqp','MaxIterations',1000);

% Use the "fmincon" function to minimize the function
[xmin,fval,exitflag,output] = fmincon(@(x) fmat(x(1),x(2)),x0,[],[],[],[],lb,ub,[],options);

% Print the results
disp(['Minimum value: ' num2str(fval)]);
disp(['Minimum point: (' num2str(xmin(1)) ', ' num2str(xmin(2)) ')']);
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In this example, the "syms" function is used to define the symbolic function "f". Then, the "matlabFunction" function is used to convert the symbolic function to a MATLAB function that can be used with the optimization algorithm.

The "fmincon" function is then used to find the minimum of the function. The syntax of the "fmincon" function is as follows:

main.m
[xmin,fval,exitflag,output] = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options)
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where "fun" is the objective function, "x0" is the initial guess for the solution, "lb" and "ub" are the lower and upper bounds for the solution, and "options" are the options for the optimization algorithm. The output variables "xmin" and "fval" are the minimum point and value of the function, respectively.

The optimization algorithm used in this example is the sequential quadratic programming ("sqp") algorithm, which is one of the many optimization algorithms available in Matlab. The "MaxIterations" option sets the maximum number of iterations for the algorithm.

The results of the optimization are then printed to the console using the "disp" function.