Fminunc matlab 2009
The total number of function evaluations was: Fevals = output.funcCount The function value at the solution is: fval Optimization completed because the objective function is non-decreasing inįeasible directions, to within the default value of the function tolerance,Īnd constraints are satisfied to within the default value of the constraint tolerance.Ī solution to this problem has been found at: x Local minimum found that satisfies the constraints. There are no linear equalities or inequalities or bounds, so pass for those arguments: = fmincon(fun,x0,gfun,options) So we write the constraint using the deal function to give both outputs: gfun = deal(g(x(1),x(2)),) Ĭall the nonlinear constrained solver. Solvers require that nonlinear constraint functions give two outputs: one for nonlinear inequalities, the second for nonlinear equalities. Set optimization options: use the interior-point algorithm, and turn on the display of results at each iteration: options = optimoptions( 'fmincon', 'Algorithm', 'interior-point', 'Display', 'iter') We are about to calculate the minimum that was just plotted.
The plot shows that the lowest value of the objective function within the ellipse occurs near the lower right part of the ellipse. Legend( 'constraint', 'f contours', 'minimum') Look at the contours of the objective function plotted together with the tilted ellipse f = x.*exp(-x.^2-y.^2)+(x.^2+y.^2)/20 The constraint set is the interior of a tilted ellipse. You can see both methods produced identical answers, so use whichever one you find most convenient.Ĭonstrained Optimization Example: InequalitiesĬonsider the above problem with a constraint: Run the optimization: = nestedbowlpeak(a,b,c,x0,options) The outer function, nestedbowlpeak, calls fminunc and passes the objective function, nestedfun.ĭefine the parameters, initial guess, and options: a = 2 In this method, the parameters (a,b,c) are visible to the nested objective function called nestedfun. %NESTEDBOWLPEAK Nested function for parameter passing in TUTDEMO. Options = optimoptions( 'fminunc', 'Algorithm', 'quasi-newton') Ĭonsider the following function that implements the objective as a nested function type nestedbowlpeakįunction = nestedbowlpeak(a,b,c,x0,options) %BOWLPEAKFUN Objective function for parameter passing in TUTDEMO. Suppose we have a MATLAB file objective function called bowlpeakfun defined as: type bowlpeakfun This function is a shifted and scaled version of the original objective function. We parameterize the function with (a,b,c) in the following way: We show two different ways of doing this - using a MATLAB file, or using a nested function.Ĭonsider the objective function from the previous section: We will now pass extra parameters as additional arguments to the objective function. Unconstrained Optimization with Additional Parameters
The total number of function evaluations is: output.funcCount We will use the number of function evaluations as a measure of efficiency in this example. The function value at the solution is: uncf = fval The default value of the function tolerance. Optimization completed because the size of the gradient is less than Iteration Func-count f(x) Step-size optimality View the iterations as the solver calculates: options.Display = 'iter' Ĭall fminunc, an unconstrained nonlinear minimizer: = fminunc(fun,x0,options) Set optimization options to not use fminunc's default large-scale algorithm, since that algorithm requires the objective function gradient to be provided: options = optimoptions( 'fminunc', 'Algorithm', 'quasi-newton') For now, this function is simple enough to define as an anonymous function: fun = f(x(1),x(2)) Usually you define the objective function as a MATLAB file. The plot shows that the minimum is near the point (-1/2,0). Plot the function to get an idea of where it is minimized f = x.*exp(-x.^2-y.^2)+(x.^2+y.^2)/20 Consider the problem of finding a minimum of the function: