# Nonsingularity Conditions for Multifunctions

Article

DOI: 10.1023/A:1008757630213

- Cite this article as:
- Levy, A.B. Set-Valued Analysis (1999) 7: 89. doi:10.1023/A:1008757630213

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## Abstract

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.

coderivativeouter graphical derivativestrict derivativepseudo-Lipschitzupper Lipschitzinverse mapping theoremoptimal solutionstationary pointsensitivity analysis

## Copyright information

© Kluwer Academic Publishers 1999