Basic Convex Analysis in Metric Spaces with Bounded Curvature
本文在曲率有上界的Alexandrov空间中，定义了基于投影和法锥的次梯度，证明了其存在性，并给出了最小化两个凸函数之和的必要最优性条件。
.Differentiable structure ensures that many of the basics of classical convex analysis extend naturally from Euclidean space to Riemannian manifolds. Without such structure, however, extensions are more challenging. Nonetheless, in Alexandrov spaces with curvature bounded above (but possibly positive), we develop several basic building blocks. We define subgradients via projection and the normal cone, prove their existence, and relate them to the classical affine minorant property. Then, in what amounts to a simple calculus or duality result, we develop a necessary optimality condition for minimizing the sum of two convex functions.Keywordssubdifferentialnormal coneAlexandrov spacesMSC codes65K1053C20