Multistart method

Because software to find local solutions of NLP problems has become so efficient and widely available, multistart methods, which attempt to find a global optimum by starting the search from many starting points, have also become more effective. As discussed briefly in Section 8.10, using different starting points is a common and easy way to explore the possibility of local optima. This section considers multistart methods for unconstrained problems without discrete variables that use randomly chosen starting points, as described in Rinnooy Kan and Timmer (1987, 1989) and more recently in Locatelli and Schoen (1999). We consider only unconstrained problems, but constraints can be incorporated by including them in a penalty function (see Section 8.4). 

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