Mathematical Sciences: Normal Cone Formulas and Calculus of Subderivatives with Applications to Optimization and Nonsmooth Analysis

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This project will provide sufficiently delicate infinite dimensional analogues of Clarke and Rockafellar non- differentiable calculus to allow its application in infinite dimensional optimization and geometry of normed spaces. The novelty of this approach lies in attempting to provide the subgradient formulas and normal cone formulas involving exact subdifferentials and exact normals. Previous work by Treiman, and by the Russian school around Ioffe, Kruger and others has always used much less satisfactory approximate subderivatives. Up to date, the investigator has investigated the case of reflexive spaces obtaining, in cooperation with Borwein, an exact basis of his now standard theory. She now proposes a general research program of building a comprehensive calculus of exact subdifferentials in Banach spaces with smooth norms. This research is part of nonlinear analysis with potential applications to optimization and control theory.