Nonsingularity Conditions for Multifunctions
- A. B. Levy
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We discuss three different characterizations of continuity properties for general multifunctions S : Rd ⇒ Rn. 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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- Nonsingularity Conditions for Multifunctions
Volume 7, Issue 1 , pp 89-99
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
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- outer graphical derivative
- strict derivative
- upper Lipschitz
- inverse mapping theorem
- optimal solution
- stationary point
- sensitivity analysis
- A. B. Levy (1)
- Author Affiliations
- 1. Department of Mathematics, Bowdoin College, Brunswick, ME, 04011, U.S.A.