Abstract
AbstractManifold 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.
Funder
National Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
Subject
Management Science and Operations Research
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