minimize with nondefault options with 9 variables in matlab

To minimize a function with nondefault options in MATLAB with 9 variables, you can use the fmincon function. This function allows you to specify various constraints and options for the optimization.

Here's an example of how to set up and solve a minimization problem with 9 variables using fmincon:

main.m
% Define the objective function
fun = @(x) sum(x.^2);

% Define the number of variables
nVars = 9;

% Define the lower and upper bounds for each variable
lb = zeros(nVars, 1);
ub = ones(nVars, 1);

% Define any additional constraints (if needed), e.g., linear equality or inequality constraints

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

% Solve the optimization problem
x0 = zeros(nVars, 1);  % Initial guess for the variables
[xMin, fMin] = fmincon(fun, x0, [], [], [], [], lb, ub, [], options);
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In this example, the objective function is defined as the sum of squares of the variables (fun = @(x) sum(x.^2)). The lower and upper bounds for each variable are set to [0, 1]. Additional constraints can be added as needed by specifying the appropriate matrices.

The optimoptions function is used to specify the options for the optimization. In the example, we set options such as displaying the iteration information and setting a maximum number of iterations.

Finally, the fmincon function is called with the objective function, initial guess for the variables, lower and upper bounds, additional constraints (if any), and the options. The solution is returned in xMin and the minimum value of the objective function is returned in fMin.