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Riemannian Optimization and Its ApplicationsIntroduction

Riemannian Optimization and Its Applications: Introduction [In this chapter, we focus on unconstrained and constrained minimization problems involving a quadratic function as simple examples of optimization problems. Then, we observe that a problem with the constraint that the sum of the squares of its decision variables should be one can be regarded as an unconstrained minimization problem on the unit sphere; this is one of the simplest examples of a Riemannian optimization problem. The steepest descent method on the sphere is also presented as an introduction to Riemannian optimization algorithms.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Riemannian Optimization and Its ApplicationsIntroduction

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Publisher
Springer International Publishing
Copyright
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
ISBN
978-3-030-62389-0
Pages
1 –11
DOI
10.1007/978-3-030-62391-3_1
Publisher site
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Abstract

[In this chapter, we focus on unconstrained and constrained minimization problems involving a quadratic function as simple examples of optimization problems. Then, we observe that a problem with the constraint that the sum of the squares of its decision variables should be one can be regarded as an unconstrained minimization problem on the unit sphere; this is one of the simplest examples of a Riemannian optimization problem. The steepest descent method on the sphere is also presented as an introduction to Riemannian optimization algorithms.]

Published: Feb 18, 2021

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