论文标题
HADAMARD空间和缩放问题的凸分析
Convex analysis on Hadamard spaces and scaling problems
论文作者
论文摘要
在本文中，我们介绍了哈达姆空间上的地质凸优化的有限/无界测定。在欧几里得凸优化中，衰退函数是研究无限制的基本工具，并提供了目标函数的legendre-fenchel结合物的域。在Hadamard空间中，渐近斜率函数（Kapovich，Leeb和Millson 2009）是Infinity在Infinity处的边界上的一个功能，起着衰退功能的作用。我们通过凸分析和优化扩展了这一概念，并为Hadamard空间上的地质凸优化的无限确定开发了凸分析基础，尤其是在非阳性曲率的对称空间上。我们解释了我们开发的理论是如何应用于操作员的规模和对群轨道的相关优化的，这是我们的动机。
In this paper, we address the bounded/unbounded determination of geodesically convex optimization on Hadamard spaces. In Euclidean convex optimization, the recession function is a basic tool to study the unboundedness, and provides the domain of the Legendre-Fenchel conjugate of the objective function. In a Hadamard space, the asymptotic slope function (Kapovich, Leeb, and Millson 2009), which is a function on the boundary at infinity, plays a role of the recession function. We extend this notion by means of convex analysis and optimization, and develop a convex analysis foundation for the unbounded determination of geodesically convex optimization on Hadamard spaces, particularly on symmetric spaces of nonpositive curvature. We explain how our developed theory is applied to operator scaling and related optimization on group orbits, which are our motivation.
