Abstract
In the following nine chapters we study optimization problems whose formulations contain minimization and maximization operations in their description — optimization problems with a two-level structure. In many instances, these problems include optimal-value functions that are not necessarily differentiable and hence difficult to work with. In this chapter we highlight a number of important properties of optimal-value functions that derive from results by Clarke [C9], Gauvin-Dubeau [G4], Fiacco [F3], and Hogan [H12] on differentiable stability analysis for nonlinear programs. These results provide the basis for several computational techniques discussed presently.
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© 1997 Springer Science+Business Media New York
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Shimizu, K., Ishizuka, Y., Bard, J.F. (1997). Optimal-Value Functions. In: Nondifferentiable and Two-Level Mathematical Programming. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-6305-1_6
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DOI: https://doi.org/10.1007/978-1-4615-6305-1_6
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7895-2
Online ISBN: 978-1-4615-6305-1
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