幾何学と非凸最適化 Geometry and Non-Convex Optimization (Springer Optimization and Its Applications 223) （2025. xiv, 895 S. XIV, 895 p. 24 illus., 15 illus. in color. 235 mm）

Herausgegeben:Pardalos, Panos M./ Rassias, Themistocles M.

SPRINGER, BERLIN; SPRINGER NATURE SWITZERLAND; SPRING（2025発売）

SPRINGER, BERLIN; SPRINGER NATURE SWITZERLAND; SPRING（2025発売）

• 製本 Hardcover:ハードカバー版／ページ数 796 p.
• 言語 ENG
• 商品コード 9783031870569

Full Description

This book offers a comprehensive exploration of the dynamic intersection between geometry and optimization. It delves into the intricate study of Hermite-Hadamard inequalities, Hilbert type integral inequalities, and variational inequalities, providing a rich tapestry of theoretical insights and practical applications.

Readers will encounter a diverse array of topics, including the bounds for the unweighted Jensen's gap of absolutely continuous functions and the properties of Barrelled and Bornological locally convex spaces. The volume also covers advanced subjects such as multiobjective mixed-integer nonlinear optimization and optimum statistical analysis on sphere surfaces. Contributions from eminent scholars provide a deep dive into C*-ternary biderivations, Erdős-Szekeres products, and variational principles, making this book a must-read for those seeking to expand their understanding of these complex fields.

Ideal for researchers and scholars in mathematics and optimization, this volume is an invaluable resource for anyone interested in the latest developments in geometry and nonconvex optimization. Whether you are a seasoned academic or a graduate student, this book will enhance your knowledge and inspire further research in these fascinating domains.

Contents

Preface.- Chapter 1 Hermite-Hadamard Like Inequalities Involving Generalized Bi-Convex Functions.- Chapter 2 Some properties of Barrelled and of Bornological locally convex spaces over an arbitrary complete valued field.- Chapter 3 Bounds for the Unweighted Jensen's Gap of Absolutely Continuous Functions.- Chapter 4 Test Instances for Multiobjective Mixed-Integer Nonlinear Optimization.- Chapter 5 A trace operator for weighted Sobolev spaces.- Chapter 6 Common fixed point results for Meir-Keeler type contraction mappings.- Chapter 7 Optimum Statistical Analysis on Sphere Surface.- Chapter 8 New Generalized Ostrowski Type Fractional Integral Inequalities.- Chapter 9 Genaralized Fractional Hilbert Type Integral Inequalities in Banach Spaces.- Chapter 10 Ternary derivation-homomorphism functional inequalities.- Chapter 11 C*-ternary biderivations and C*-ternary bihomomorphisms.- Chapter 12 A Survey of Erdős-Szekeres Products.- Chapter 13 Recent developments in general quasi variational inequality.- Chapter 14 General Variational Inequalities and Optimization.- Chapter 15 Characterizations and Set Theoretic Properties of Some Generalized Open and Fat Sets in Relator Spaces.- Chapter 16 Direct Continuity Properties of Relations in Relator Spaces.- Chapter 17 Variational Principles and Fixed Points in Symmetric Structures.- Chapter 18 Sequential Coercivity over Q-Ordered Q-Metric Spaces.- Chapter 19 A Hardy-Hilbert's Integral Inequality with the Internal Variables Involving Two Derivative Functions.