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An introduction to optimization on smooth manifolds

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	An introduction to optimization on smooth manifolds/ Nicolas Boumal.
作者:	Boumal, Nicolas,
出版者:	Cambridge ;Cambridge University Press, : 2023.,
面頁冊數:	xviii, 338 p. :ill., digital ;27 cm.
附註:	Title from publisher's bibliographic system (viewed on 09 Mar 2023).
內容註:	Simple examples -- Embedded geometry : first order -- First-order optimization algorithms -- Embedded geometry : second order -- Second-order optimization algorithms -- Embedded submanifolds : examples -- General manifolds -- Quotient manifolds -- Additional tools -- Geodesic convexity.
標題:	Manifolds (Mathematics) -
電子資源:	https://doi.org/10.1017/9781009166164
ISBN:	9781009166164

An introduction to optimization on smooth manifolds
Boumal, Nicolas,1987-

An introduction to optimization on smooth manifolds[electronic resource] /Nicolas Boumal. - Cambridge ;Cambridge University Press,2023. - xviii, 338 p. :ill., digital ;27 cm.

Title from publisher's bibliographic system (viewed on 09 Mar 2023).

Simple examples -- Embedded geometry : first order -- First-order optimization algorithms -- Embedded geometry : second order -- Second-order optimization algorithms -- Embedded submanifolds : examples -- General manifolds -- Quotient manifolds -- Additional tools -- Geodesic convexity.

Optimization on Riemannian manifolds-the result of smooth geometry and optimization merging into one elegant modern framework-spans many areas of science and engineering, including machine learning, computer vision, signal processing, dynamical systems and scientific computing. This text introduces the differential geometry and Riemannian geometry concepts that will help students and researchers in applied mathematics, computer science and engineering gain a firm mathematical grounding to use these tools confidently in their research. Its charts-last approach will prove more intuitive from an optimizer's viewpoint, and all definitions and theorems are motivated to build time-tested optimization algorithms. Starting from first principles, the text goes on to cover current research on topics including worst-case complexity and geodesic convexity. Readers will appreciate the tricks of the trade for conducting research and for numerical implementations sprinkled throughout the book.

ISBN: 9781009166164Subjects--Topical Terms:

612607
Manifolds (Mathematics)

LC Class. No.: QA613 / .B68 2023

Dewey Class. No.: 516.36

An introduction to optimization on smooth manifolds
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520 $a Optimization on Riemannian manifolds-the result of smooth geometry and optimization merging into one elegant modern framework-spans many areas of science and engineering, including machine learning, computer vision, signal processing, dynamical systems and scientific computing. This text introduces the differential geometry and Riemannian geometry concepts that will help students and researchers in applied mathematics, computer science and engineering gain a firm mathematical grounding to use these tools confidently in their research. Its charts-last approach will prove more intuitive from an optimizer's viewpoint, and all definitions and theorems are motivated to build time-tested optimization algorithms. Starting from first principles, the text goes on to cover current research on topics including worst-case complexity and geodesic convexity. Readers will appreciate the tricks of the trade for conducting research and for numerical implementations sprinkled throughout the book.
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