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Convex Analysis and Optimization in Hadamard Spaces (De Gruyter Series in Nonlinear Analysis and Applications, 22) - Miroslav Bacak September 29, 2014 PDF  BOOKS
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Convex Analysis and Optimization in Hadamard Spaces (De Gruyter Series in Nonlinear Analysis and Applications, 22)
Author: Miroslav Bacak
Year: September 29, 2014
Format: PDF
File size: PDF 1.3 MB
Language: English



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Book Description: Convex Analysis and Optimization in Hadamard Spaces (De Gruyter Series in Nonlinear Analysis and Applications, 22) Author: Miroslav Bacak September 29, 2014 Pages: Publisher: De Gruyter Summary: In the past two decades, convex analysis and optimization have evolved significantly in Hadamard spaces, providing a comprehensive understanding of the subject. This book offers a systematic account of the subject, delving into the role of Hadamard spaces in geometry and geometric group theory. It highlights the appropriateness of Hadamard spaces for the theory of convex sets and functions outside linear spaces, making it an essential read for graduate students, researchers, and advanced undergraduate students interested in analysis and optimization. Plot: The book begins by introducing the concept of Hadamard spaces, complete geodesic spaces with non-positive curvature, including Hilbert spaces, Hadamard manifolds, and Euclidean buildings. The author delves into the analytical results that emerged in the 1990s, showcasing the significance of convexity in the geometry of Hadamard spaces. This section sets the foundation for the subsequent chapters, which explore the application of optimization methods in computational phylogenetics.
Convex Analysis and Optimization in Hadamard Spaces (De Gruyter Series in Nonlinear Analysis and Applications, 22) Автор: Мирослав Бакак 29.09.2014 Страницы: Издатель: De Gruyter Резюме: За последние два десятилетия выпуклый анализ и оптимизация значительно эволюционировали в пространствах Адамара, обеспечивая всестороннее понимание предмет. Эта книга предлагает систематическое изложение предмета, углубляясь в роль пространств Адамара в геометрии и геометрической теории групп. Он подчеркивает уместность пространств Адамара для теории выпуклых множеств и функций вне линейных пространств, что делает его важным чтением для аспирантов, исследователей и продвинутых студентов, заинтересованных в анализе и оптимизации. Сюжет: Книга начинается с введения понятия пространств Адамара, полных геодезических пространств с неположительной кривизной, включая гильбертовы пространства, многообразия Адамара и евклидовы построения. Автор углубляется в аналитические результаты, появившиеся в 1990-е годы, демонстрируя значение выпуклости в геометрии пространств Адамара. Этот раздел закладывает основу для последующих глав, в которых исследуется применение методов оптимизации в вычислительной филогенетике.
Análisis y optimización de Convex en Espacios Hadamard (De Gruyter Series in Nonlinear Analysis and Applications, 22) Autor: Miroslav Bakak 29.09.2014 Páginas: Editor: De Gruyter Resumen: En las últimas dos décadas, el análisis convexo y la optimización han evolucionado significativamente en los espacios de Adamar, proporcionando una comprensión integral del tema. Este libro ofrece una presentación sistemática del tema, profundizando en el papel de los espacios de Adamar en la geometría y la teoría geométrica de los grupos. Destaca la idoneidad de los espacios de Adamar para la teoría de conjuntos convexos y funciones fuera de los espacios lineales, lo que la convierte en una importante lectura para estudiantes de posgrado, investigadores y estudiantes avanzados interesados en el análisis y la optimización. Trama: libro comienza introduciendo la noción de espacios de Adamar llenos de espacios geodésicos con curvatura no positiva, incluyendo espacios de Hilbert, multitudes de Adamar y construcciones euclidianas. autor profundiza en los resultados analíticos aparecidos en la década de 1990, demostrando el significado de la protuberancia en la geometría de los espacios de Adamar. Esta sección sienta las bases para capítulos posteriores que exploran la aplicación de técnicas de optimización en la filogenética computacional.
Convex Analysis and Valorization in Hadamard Space (De Gruyter Series in Nonlinear Analysis and Application, 22) Autore: Miroslav Bakak Pagine: Editore: De Gruyter Curriculum - Analisi convulsive negli ultimi due decenni e l'ottimizzazione si è evoluta notevolmente negli spazi di Adamar, fornendo una piena comprensione del soggetto. Questo libro propone una descrizione sistematica dell'oggetto, approfondendo il ruolo degli spazi Adamar nella geometria e nella teoria geometrica dei gruppi. Sottolinea l'appropriatezza degli spazi Adamar per la teoria delle molteplici e funzioni fuori dagli spazi lineari, che lo rende una lettura importante per studenti di laurea, ricercatori e studenti avanzati interessati ad analisi e ottimizzazione. Il libro inizia introducendo la nozione di spazi Adamar pieni di spazi geodesici con curvatura incompleta, inclusi lo spazio gilberth, la diversità di Adamar e l'euclide. L'autore approfondisce i risultati analitici emersi negli anni Novanta, dimostrando il valore di convulsione nella geometria degli spazi Adamar. Questa sezione fornisce le basi per i successivi capitoli che esaminano l'utilizzo delle tecniche di ottimizzazione nella filogenetica computazionale.
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ハダマール空間における凸解析と最適化(非線形解析とアプリケーションにおけるDe Gruyterシリーズ、22)著者:Miroslav Bakak 29.09.2014 Pages: Publisher: De Gruyter Summary:過去20間、凸解析と最適化は大きく進化しましたAdamakは、主題の包括的な理解を提供する、araをスペースします。本書では、幾何学や幾何学的グループ理論におけるハダマール空間の役割を掘り下げ、主題を体系的に解説している。これは、線形空間外の凸集合や関数の理論のためのハダマール空間の適切性を強調しており、解析と最適化に関心のある大学院生、研究者、上級学生にとって重要なリーディングとなっている。プロット:この本は、ハダマール空間の概念、ヒルベルト空間、ハダマール多様体、ユークリッド構造を含む非正曲率の完全な測地空間を紹介することから始まります。著者は1990代に登場した分析結果を詳しく調べ、ハダマール空間の幾何学における凸性の価値を示している。このセクションでは、計算系統学における最適化技術の応用を探求する後続の章の基礎を説明します。

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