Continuous Selections of Solutions for Locally Lipschitzian Equations

This paper answers in the affirmative the long-standing question of nonlinear analysis, concerning the existence of a continuous single-valued local selection of the right inverse to a locally Lipschitzian mapping. Moreover, we develop a much more general result, providing conditions for the existen...

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Bibliographic Details
Published in:	Journal of optimization theory and applications Vol. 185; no. 3; pp. 679 - 699
Main Authors:	Arutyunov, Aram V., Izmailov, Alexey F., Zhukovskiy, Sergey E.
Format:	Journal Article
Language:	English
Published:	New York Springer US 01-06-2020 Springer Nature B.V
Subjects:	Applications of Mathematics Calculus of Variations and Optimal Control; Optimization Engineering Mapping Mathematics Mathematics and Statistics Nonlinear analysis Operations Research/Decision Theory Optimization Questions Theorems Theory of Computation Topology 58C15 Nonlinear equation 49J53 Clarke’s generalized Jacobian Inverse function theorem 49J52 Locally Lipschitzian mapping Hadamard’s theorem 47J07 Continuous selection of solutions 47J05
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