A Brief Introduction to Manifold Optimization
A Brief Introduction to Manifold Optimization
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DOI：
10.1007/s40305-020-00295-9
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发表时间：
2020-04-04
影响因子：
1.4
通讯作者：
Yuan, Ya-Xiang
中科院分区：
文献类型：
--
作者：
Hu, Jiang;Liu, Xin;Yuan, Ya-Xiang
流形优化在计算和应用数学、统计学、工程学、机器学习、物理学、化学等领域普遍存在，其中一个主要挑战通常是流形约束的非凸性。利用流形的几何性质，可以将一大类约束优化问题看作流形上的无约束优化问题。从这个角度出发，研究了流形优化的内在结构、最优性条件和数值算法。最后介绍了流形优化理论研究的一些新进展。
Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry, etc. One of the main challenges usually is the non-convexity of the manifold constraints. By utilizing the geometry of manifold, a large class of constrained optimization problems can be viewed as unconstrained optimization problems on manifold. From this perspective, intrinsic structures, optimality conditions and numerical algorithms for manifold optimization are investigated. Some recent progress on the theoretical results of manifold optimization is also presented.