use fmincon in matlab to optimize a cubic function in matlab

To use the fmincon function in MATLAB to optimize a cubic function, you need to define the objective function and any constraints.

Here's an example of how you can optimize a cubic function using fmincon:

main.m
% Define the objective function
objective = @(x) x^3 - 6*x^2 + 11*x - 6;

% Set up initial guess and constraints
x0 = 0; % initial guess
lb = -10; % lower bound
ub = 10; % upper bound
A = []; % linear inequality constraints matrix
b = []; % linear inequality constraints vector
Aeq = []; % linear equality constraints matrix
beq = []; % linear equality constraints vector
nonlcon = []; % nonlinear constraints

% Perform optimization using fmincon
[x, fval] = fmincon(objective, x0, A, b, Aeq, beq, lb, ub, nonlcon);

disp(['Optimized x: ', num2str(x)]);
disp(['Objective function value: ', num2str(fval)]);
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In this example, x is the variable being optimized, and objective is the objective function (in this case, a cubic function). The lb and ub variables define the lower and upper bounds on x. The other variables (A, b, Aeq, beq, and nonlcon) are used for setting up any constraints you might have.

The fmincon function will try to find the optimal value of x that minimizes the objective function.

Note that this is just a simple example, and you can customize it based on your specific problem.

Make sure you have the Optimization Toolbox installed in MATLAB to use fmincon.

I hope this helps you get started with using fmincon to optimize a cubic function in MATLAB!