![]() ![]() All the tutorials are completely free.Fmincon (Optimization Toolbox) Optimization Toolboxįind a minimum of a constrained nonlinear multivariable function This website contains more than 200 free tutorials! Every tutorial is accompanied by a YouTube video. This function is called from the following script. The code lines 29-31 are used to code the cost function. ![]() The code lines 14-15 are used to incorporate the constraints of the optimization problem ( 8). We briefly comment upon the main changes made with respect with the previous function version. The modified function “minimize_cost_function” takes the following form:įunction =minimize_cost_function(x0)į= The cost function ( 9), can also be written as follows: Notice that now, in sharp contrast to the previously considered least-squares problem, we have constraints. ![]() Let us know write the MATLAB code that will solve the following optimization problem: Finally, the code line 15 is used to compare “solution” with the exact (least-squares) solution. The code line is used to compute the least-squares solution defined by the equation ( 7). We use this code line to call the function “minimize_cost_function” that is stored in the MATLAB path, so you can call this function from another script. The code line 9 is used to solve the problem. Notice that we choose these quantities as random matrices/vectors (type “help rand” and “help randn” to see basic descriptions of these functions). The code lines 2-6 are used to define the coefficient matrix A, the vector and an initial solution guess. Norm(solution-exact_solution,2)/norm(exact_solution,2)Ī few comments are in order. % compare the computed solution with the exact solution % generate A coefficient matrix and y vector The other arguments are used to define the initial solution “x0” and constraints.Īfter saving the function “minimize_cost_function.m” in a folder and after adding this folder to the MATLAB path (do not forget to do this!), we can call this function from another MATLAB script given below The first argument of the fmincon() function is This argument is used to tell fmincon() that the cost function is defined in the function “cost_function(x)” that is defined on the code lines 26-32. We use the code line 23 to solve the problem. The first option tells MATLAB that we plan to use the build-in “fmincon” function to solve the problem. We we the option “Display” to “iter” to monitor and plot the optimization progress. We can select an algorithm, set the optimization tolerances, or even tell the optimizer to use the gradient of the cost function. The code line 21 defines the options for the solver. However, in our case, we are considering an unconstrained problem, so these constraints are left empty. We can use the code lines 10-15 to define the constraints for the optimizer. ![]() The solution to the optimization problem is stored in “solution”. On the code line 1, we can see that this function returns several variables. That is, the name of the function should correspond to the name used in the function declaration/definition. It is important to save this function in a new folder, and to name this function ” minimize_cost_function.m”. % notice that this function can access the arguments of the function % algorithm can be 'interior-point', 'SQP','active set', and 'trust region reflective' % x C(x) <= 0, Ceq(x) = 0 (nonlinear constraints) % min J(x) subject to: Aineq*x <= Bineq, Aeq*x = Beq (linear constraints) % fmincon attempts to solve problems of the form: % summary of the optimization problem-general form ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |