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

这个项目将提供足够精致的无限 Clarke和Rockafellar的一维类似物 微积分允许它的应用在无限 维数优化和赋范空间几何。 的 这种方法的新奇在于试图提供 次梯度公式和法锥公式 次微分和精确法线。 Treiman以前的工作， 约菲附近的俄罗斯学校，克鲁格和其他人 总是使用不太令人满意的近似次导数。 到目前为止，调查员已经调查了 自反空间获得，在与Borwein合作，一个确切的 这是他现在的标准理论。她现在建议一位将军 建立一个综合的精确微积分的研究计划 Banach空间中具有光滑范数的次微分 本研究属于非线性分析的一部分， 应用于优化和控制理论。

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.