Set-Valued Analysis

, Volume 7, Issue 1, pp 89–99

Nonsingularity Conditions for Multifunctions

  • A. B. Levy

DOI: 10.1023/A:1008757630213

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


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.

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

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • A. B. Levy
    • 1
  1. 1.Department of MathematicsBowdoin CollegeBrunswickU.S.A.

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