Optimization on Manifolds
Riemannian gradient methods and retractions.
Optimization on Manifolds. Riemannian gradient methods and retractions.
Foundations and canonical references
The standard treatments of optimization on manifolds approach the subject from complementary angles. Absil, Optimization Algorithms on Matrix Manifolds (2008) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Boumal, An Introduction to Optimization on Smooth Manifolds (2023) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for optimization on manifolds include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2008Optimization Algorithms on Matrix Manifoldsabsil-2008, mahony-2008, sepulchre-2008
- textbook · primary · 2023An Introduction to Optimization on Smooth Manifoldsboumal-2023
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