What Is Optimization Toolbox?

Unconstrained Optimizationvariables, x, in turn and calculating the rate of change in the objectivefunction.At each major iteration, k, a line search is performed in the direction(3-7)The quasi-Newton method is illustrated bythesolutionpathonRosenbrock’sfunction in Figure 3-2, BFGS Method on Rosenbrock’s Function. The methodis able to follow the shape of the valley and converges to the minimum after140 function evaluations using only finite difference gradients.Figure 3-2:BFGS Method on Rosenbrock’s FunctionLine SearchLine search is a search method that is used as part of a larger optimizationalgorithm. At each step of the main algorithm, the line-search methodsearches along the line containing the current point, x k,paralleltothesearchdirection, which is a vector determined by the main algorithm. That is, themethod finds the next iterate of the formwhere denotes the current iterate, d kis the search direction, and alpha *is a scalar step length parameter.(3-8)3-9