What Is Optimization Toolbox?

Optimization Tool Examplesmax Line search Directional First-orderIter F-count f(x) constraint steplength derivative optimality0 3 10 21 6 4.84298 -0.1322 1 -3.4 1.742 9 4.0251 -0.01168 1 -0.78 4.083 12 2.42704 -0.03214 1 -1.37 1.094 15 2.03615 -0.004728 1 -0.373 0.9955 18 2.00033 -5.596e-005 1 -0.0357 0.06646 21 2 -5.327e-009 1 -0.000326 0.0005227 24 2 -2.22e-016 1 -2.69e-008 1.21e-008Optimization terminated: first-order optimality measure lessthan options.TolFun and maximum constraint violation is lessthan options.TolCon.Active inequalities (to within options.TolCon = 1e-006):lower upper ineqlin ineqnonlin34Reference[1] Schittkowski, K., “More Test Examples for Nonlinear ProgrammingCodes,” Lecture Notes in Economics and Mathematical Systems, Number 282,Springer, p. 45, 1987.Optimization Tool with the lsqlin SolverThisexampleshowshowtousetheOptimizationTooltosolvethe“Optimization Example” on page 1-4.The ProblemThe problem in this example is to find the point on the planethat is closest to the origin. The easiest way to solve this problem is tominimize the square of the distance from a pointon the planeto the origin, which returns the same optimal point as minimizing the actualdistance. Since the square of the distance from an arbitrary pointto the origin is, you can describe the problem as follows:5-51