Moment and Polynomial Optimization

ยท SIAM
แƒ”แƒšแƒฌแƒ˜แƒ’แƒœแƒ˜
483
แƒ’แƒ•แƒ”แƒ แƒ“แƒ˜
แƒ›แƒ˜แƒกแƒแƒฆแƒ”แƒ‘แƒ˜
แƒ แƒ”แƒ˜แƒขแƒ˜แƒœแƒ’แƒ”แƒ‘แƒ˜ แƒ“แƒ แƒ›แƒ˜แƒ›แƒแƒฎแƒ˜แƒšแƒ•แƒ”แƒ‘แƒ˜ แƒ“แƒแƒฃแƒ“แƒแƒกแƒขแƒฃแƒ แƒ”แƒ‘แƒ”แƒšแƒ˜แƒ ย แƒจแƒ”แƒ˜แƒขแƒงแƒ•แƒ”แƒ— แƒ›แƒ”แƒขแƒ˜

แƒแƒ› แƒ”แƒšแƒฌแƒ˜แƒ’แƒœแƒ˜แƒก แƒจแƒ”แƒกแƒแƒฎแƒ”แƒ‘

Moment and polynomial optimization is an active research field used to solve difficult questions in many areas, including global optimization, tensor computation, saddle points, Nash equilibrium, and bilevel programs, and it has many applications. The author synthesizes current research and applications, providing a systematic introduction to theory and methods, a comprehensive approach for extracting optimizers and solving truncated moment problems, and a creative methodology for using optimality conditions to construct tight Moment-SOS relaxations.

This book is intended for applied mathematicians, engineers, and researchers entering the field. It can be used as a textbook for graduate students in courses on convex optimization, polynomial optimization, and matrix and tensor optimization.

แƒจแƒ”แƒแƒคแƒแƒกแƒ”แƒ— แƒ”แƒก แƒ”แƒšแƒฌแƒ˜แƒ’แƒœแƒ˜

แƒ’แƒ•แƒ˜แƒ—แƒฎแƒแƒ แƒ˜แƒ— แƒ—แƒฅแƒ•แƒ”แƒœแƒ˜ แƒแƒ–แƒ แƒ˜.

แƒ˜แƒœแƒคแƒแƒ แƒ›แƒแƒชแƒ˜แƒ แƒฌแƒแƒ™แƒ˜แƒ—แƒฎแƒ•แƒแƒกแƒ—แƒแƒœ แƒ“แƒแƒ™แƒแƒ•แƒจแƒ˜แƒ แƒ”แƒ‘แƒ˜แƒ—

แƒกแƒ›แƒแƒ แƒขแƒคแƒแƒœแƒ”แƒ‘แƒ˜ แƒ“แƒ แƒขแƒแƒ‘แƒšแƒ”แƒขแƒ”แƒ‘แƒ˜
แƒ“แƒแƒแƒ˜แƒœแƒกแƒขแƒแƒšแƒ˜แƒ แƒ”แƒ— Google Play Books แƒแƒžแƒ˜ Android แƒ“แƒ iPad/iPhone แƒ›แƒแƒฌแƒงแƒแƒ‘แƒ˜แƒšแƒแƒ‘แƒ”แƒ‘แƒ˜แƒกแƒ—แƒ•แƒ˜แƒก. แƒ˜แƒก แƒแƒ•แƒขแƒแƒ›แƒแƒขแƒฃแƒ แƒแƒ“ แƒ’แƒแƒœแƒแƒฎแƒแƒ แƒชแƒ˜แƒ”แƒšแƒ”แƒ‘แƒก แƒกแƒ˜แƒœแƒฅแƒ แƒแƒœแƒ˜แƒ–แƒแƒชแƒ˜แƒแƒก แƒ—แƒฅแƒ•แƒ”แƒœแƒก แƒแƒœแƒ’แƒแƒ แƒ˜แƒจแƒ—แƒแƒœ แƒ“แƒ แƒกแƒแƒจแƒฃแƒแƒšแƒ”แƒ‘แƒแƒก แƒ›แƒแƒ’แƒชแƒ”แƒ›แƒ—, แƒฌแƒแƒ˜แƒ™แƒ˜แƒ—แƒฎแƒแƒ— แƒกแƒแƒกแƒฃแƒ แƒ•แƒ”แƒšแƒ˜ แƒ™แƒแƒœแƒขแƒ”แƒœแƒขแƒ˜ แƒœแƒ”แƒ‘แƒ˜แƒกแƒ›แƒ˜แƒ”แƒ  แƒแƒ“แƒ’แƒ˜แƒšแƒแƒก, แƒ แƒแƒ’แƒแƒ แƒช แƒแƒœแƒšแƒแƒ˜แƒœ, แƒ˜แƒกแƒ” แƒฎแƒแƒ–แƒ’แƒแƒ แƒ”แƒจแƒ” แƒ แƒ”แƒŸแƒ˜แƒ›แƒจแƒ˜.
แƒšแƒ”แƒžแƒขแƒแƒžแƒ”แƒ‘แƒ˜ แƒ“แƒ แƒ™แƒแƒ›แƒžแƒ˜แƒฃแƒขแƒ”แƒ แƒ”แƒ‘แƒ˜
Google Play-แƒจแƒ˜ แƒจแƒ”แƒซแƒ”แƒœแƒ˜แƒšแƒ˜ แƒแƒฃแƒ“แƒ˜แƒแƒฌแƒ˜แƒ’แƒœแƒ”แƒ‘แƒ˜แƒก แƒ›แƒแƒกแƒ›แƒ”แƒœแƒ แƒ—แƒฅแƒ•แƒ”แƒœแƒ˜ แƒ™แƒแƒ›แƒžแƒ˜แƒฃแƒขแƒ”แƒ แƒ˜แƒก แƒ•แƒ”แƒ‘-แƒ‘แƒ แƒแƒฃแƒ–แƒ”แƒ แƒ˜แƒก แƒ’แƒแƒ›แƒแƒงแƒ”แƒœแƒ”แƒ‘แƒ˜แƒ— แƒจแƒ”แƒ’แƒ˜แƒซแƒšแƒ˜แƒแƒ—.
แƒ”แƒšแƒฌแƒแƒ›แƒ™แƒ˜แƒ—แƒฎแƒ•แƒ”แƒšแƒ”แƒ‘แƒ˜ แƒ“แƒ แƒกแƒฎแƒ•แƒ แƒ›แƒแƒฌแƒงแƒแƒ‘แƒ˜แƒšแƒแƒ‘แƒ”แƒ‘แƒ˜
แƒ”แƒšแƒ”แƒฅแƒขแƒ แƒแƒœแƒฃแƒšแƒ˜ แƒ›แƒ”แƒšแƒœแƒ˜แƒก แƒ›แƒแƒฌแƒงแƒแƒ‘แƒ˜แƒšแƒแƒ‘แƒ”แƒ‘แƒ–แƒ” แƒฌแƒแƒกแƒแƒ™แƒ˜แƒ—แƒฎแƒแƒ“, แƒ แƒแƒ’แƒแƒ แƒ˜แƒชแƒแƒ Kobo eReaders, แƒ—แƒฅแƒ•แƒ”แƒœ แƒฃแƒœแƒ“แƒ แƒฉแƒแƒ›แƒแƒขแƒ•แƒ˜แƒ แƒ—แƒแƒ— แƒคแƒแƒ˜แƒšแƒ˜ แƒ“แƒ แƒ’แƒแƒ“แƒแƒ˜แƒขแƒแƒœแƒแƒ— แƒ˜แƒ’แƒ˜ แƒ—แƒฅแƒ•แƒ”แƒœแƒก แƒ›แƒแƒฌแƒงแƒแƒ‘แƒ˜แƒšแƒแƒ‘แƒแƒจแƒ˜. แƒ“แƒแƒฎแƒ›แƒแƒ แƒ”แƒ‘แƒ˜แƒก แƒชแƒ”แƒœแƒขแƒ แƒ˜แƒก แƒ“แƒ”แƒขแƒแƒšแƒฃแƒ แƒ˜ แƒ˜แƒœแƒกแƒขแƒ แƒฃแƒฅแƒชแƒ˜แƒ”แƒ‘แƒ˜แƒก แƒ›แƒ˜แƒฎแƒ”แƒ“แƒ•แƒ˜แƒ— แƒ’แƒแƒ“แƒแƒ˜แƒขแƒแƒœแƒ”แƒ— แƒคแƒแƒ˜แƒšแƒ”แƒ‘แƒ˜ แƒ›แƒฎแƒแƒ แƒ“แƒแƒญแƒ”แƒ แƒ˜แƒš แƒ”แƒšแƒฌแƒแƒ›แƒ™แƒ˜แƒ—แƒฎแƒ•แƒ”แƒšแƒ”แƒ‘แƒ–แƒ”.
แƒฃแƒ™แƒแƒœแƒแƒœแƒ แƒ™แƒแƒœแƒขแƒ”แƒœแƒขแƒ˜แƒก แƒจแƒ”แƒกแƒแƒฎแƒ”แƒ‘ แƒ›แƒแƒฎแƒกแƒ”แƒœแƒ”แƒ‘แƒ

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