國立虎尾科技大學 |

An introduction to optimization on smooth manifolds /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	An introduction to optimization on smooth manifolds // Nicolas Boumal.
作者:	Boumal, Nicolas,
面頁冊數:	1 online resource (xviii, 338 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 09 Mar 2023).
標題:	Mathematical optimization. -
電子資源:	https://doi.org/10.1017/9781009166164
ISBN:	9781009166164 (ebook)

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

An introduction to optimization on smooth manifolds /Nicolas Boumal. - 1 online resource (xviii, 338 pages) :digital, PDF file(s).

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: 9781009166164 (ebook)Subjects--Topical Terms:

527675
Mathematical optimization.

LC Class. No.: QA613 / .B68 2023

Dewey Class. No.: 516.3/6

An introduction to optimization on smooth manifolds /
LDR:02321nam a2200301 i 4500 001 1127301
003 UkCbUP
005 20230309021938.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 240926s2023||||enk o ||1 0|eng|d
020 $a 9781009166164 (ebook)
020 $z 9781009166171 (hardback)
020 $z 9781009166157 (paperback)
035 $a CR9781009166164
040 $a UkCbUP $b eng $e rda $c UkCbUP
050 0 0 $a QA613 $b .B68 2023
082 0 0 $a 516.3/6 $2 23/eng20230106
100 1 $a Boumal, Nicolas, $d 1987- $e author. $3 1446603
245 1 3 $a An introduction to optimization on smooth manifolds / $c Nicolas Boumal.
264 1 $a Cambridge ; $a New York, NY : $b Cambridge University Press, $c 2023.
300 $a 1 online resource (xviii, 338 pages) : $b digital, PDF file(s).
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Title from publisher's bibliographic system (viewed on 09 Mar 2023).
505 0 $a 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.
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.
650 0 $a Mathematical optimization. $3 527675
650 0 $a Manifolds (Mathematics) $3 672402
776 0 8 $i Print version: $z 9781009166171
856 4 0 $u https://doi.org/10.1017/9781009166164