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Nonsingularity Conditions for Multifunctions
 A. B. Levy
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We discuss three different characterizations of continuity properties for general multifunctions S : R^{d} ⇒ R^{n}. Each of these characterizations is given by the same simple nonsingularity condition, but stated in terms of three different generalized derivatives. Two of these characterizations are known, but the third is new to this paper. We discuss how all three have immediate analogues as generalized inverse mapping theorems, and we apply our new characterization to develop a fundamental and very broad sensitivity theorem for solutions to parameterized optimization problems.
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 Title
 Nonsingularity Conditions for Multifunctions
 Journal

SetValued Analysis
Volume 7, Issue 1 , pp 8999
 Cover Date
 19990301
 DOI
 10.1023/A:1008757630213
 Print ISSN
 09276947
 Online ISSN
 1572932X
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 coderivative
 outer graphical derivative
 strict derivative
 pseudoLipschitz
 upper Lipschitz
 inverse mapping theorem
 optimal solution
 stationary point
 sensitivity analysis
 Authors

 A. B. Levy ^{(1)}
 Author Affiliations

 1. Department of Mathematics, Bowdoin College, Brunswick, ME, 04011, U.S.A.