Set-Valued Analysis

, Volume 7, Issue 1, pp 89-99

First online:

Nonsingularity Conditions for Multifunctions

  • A. B. LevyAffiliated withDepartment of Mathematics, Bowdoin College

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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.

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