What Is Optimization Toolbox?

2 TutorialTypicalProblemsandHowtoDealwithThemOptimization problems can take many iterations to converge and can besensitivetonumericalproblemssuchastruncation and round-off error in thecalculation of finite-difference gradients. Most optimization problems benefitfrom good starting guesses. This improves the execution efficiency and canhelp locate the global minimum instead of a local minimum.Advanced problems are best solved by an evolutionary approach, whereby aproblem with a smaller number of independentvariablesissolvedfirst.Youcan generally use solutions from lower order problems as starting points forhigher order problems by using an appropriate mapping.The use of simpler cost functions and less stringent termination criteria in theearly stages of an optimization problem can also reduce computation time.Such an approach often produces superior results by avoiding local minima.Optimization Toolbox functions can be applied to a large variety of problems.Used with a little “conventional wisdom,” you can overcome many of thelimitations associated with optimization techniques. Additionally, youcan handle problems that are not typically in the standard form by usingan appropriate transformation. Below is a list of typical problems andrecommendations for dealing with them.TroubleshootingProblemThe solution does notappear to be a globalminimum.RecommendationThere is no guarantee that you have a global minimum unless yourproblem is continuous and has only one minimum. Starting theoptimization from a number of different starting points can help tolocate the global minimum or verify that there is only one minimum.Use different methods, where possible, to verify results.2-98