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

这个项目将提供Clarke和Rockafella不可微微积分的足够精细的无限维类似物，以允许它在无限维最优化和赋范空间的几何中应用。这种方法的创新之处在于尝试提供了涉及精确次微分和精确法线的次梯度公式和法锥公式。Treiman以及围绕Ioffe、Kruger和其他人的俄罗斯学派之前的工作总是使用不太令人满意的近似次导数。到目前为止，这位研究人员与Borwein合作，研究了自反空间的情况，获得了他现在标准理论的确切基础。她现在提出了一个一般的研究方案，即在具有光滑范数的Banach空间中建立一个全面的精确次微分演算。这项研究是非线性分析的一部分，对优化和控制理论具有潜在的应用价值。

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.