| Warga Derivate Containers and Other Generalized Differentials (2002) | |||||||||||||||
Abstract | |||||||||||||||
| This is the first of two papers devoted to recent ideas on the theory of generalized differentials with good open mapping properties. Here we will discuss "generalized differentiation theories" (abbr. GDTs), with special emphasis on the series of developments initiated by Jack Warga's pioneering work on derivate containers. In the second paper, we will focus on the most recent theory, of "path-integral generalized differentials," and prove that it has the crucial properties required for a version of the Pontryagin Maximum Principle (abbr. PMP) to exist, namely, the chain rule and the directional open mapping property. Our work continues the study of general smooth, nonsmooth, high-order, and hybrid versions of the PMP for finite-dimensional deterministic optimal control problems without state space constraints by means of a method developed by us in recent years. As explained in [11, 12, 13, 14], such versions can be derived in a unified way, by using a modified version of... | |||||||||||||||
Publication details | |||||||||||||||
| |||||||||||||||