Multidifferential Calculus: Chain Rule, Open Mapping and Transversal Intersection Theorems

  • Héctor J. Sussmann
Part of the Applied Optimization book series (APOP, volume 15)


The purpose of this note is to develop a calculus of “multidifferentials” of setvalued maps between finite-dimensional real linear spaces. This will be done by generalizing the concept of the classical differential (CD), following the ideas of F. Clarke’s theory of generalized Jacobians (CGJ’s) and J. Warga’s theory of derivate containers (WDC’s), cf. Clarke [4] and Warga [17, 18, 19, 20].


Compact Subset Open Mapping Convex Cone Closed Convex Cone Pontryagin Maximum Principle 
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Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Héctor J. Sussmann
    • 1
  1. 1.Department of MathematicsRutgers UniversityNew BrunswickUSA

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