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Erschienen in:
2000 | OriginalPaper | Buchkapitel
Unconstrained Problems
verfasst von : M. Asghar Bhatti
Erschienen in: Practical Optimization Methods
Verlag: Springer New York
Enthalten in: Professional Book Archive
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As seen in Chapter 4, it is possible to solve optimization problems by directly using the optimality conditions. However, setting up and solving the resulting nonlinear system of equations becomes very difficult as the problem size increases. Furthermore, at least for constrained problems, checking the second-order sufficient conditions is usually very difficult. In such cases, one must find all stationary points in order to be absolutely sure that a minimum has been found. Otherwise instead of a minimum point, one could actually end up with a maximum point. Clearly, finding all possible solutions for large systems of nonlinear equations is a daunting task, if not impossible.