A Brief Introduction to Manifold Optimization
arXiv:1906.05450
Abstract
Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry and 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 are also presented.
43 pages
References in corpus (4)
- Solving SDPs for synchronization and MaxCut problems via the Grothendieck inequality
- Vector Transport-Free SVRG with General Retraction for Riemannian Optimization: Complexity Analysis and Practical Implementation
- Primal-Dual Optimization Algorithms over Riemannian Manifolds: an Iteration Complexity Analysis
- Adaptive Regularized Newton Method for Riemannian Optimization