Geometry And Non Convex Optimization
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Geometry and Non-Convex Optimization
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.
Convex Optimization
Author: Stephen P. Boyd
language: en
Publisher: Cambridge University Press
Release Date: 2004-03-08
Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.
Modern Nonconvex Nondifferentiable Optimization
Author: Ying Cui
language: en
Publisher: Society for Industrial and Applied Mathematics (SIAM)
Release Date: 2022
"This monograph serves present and future needs where nonconvexity and nondifferentiability are inevitably present in the faithful modeling of real-world applications of optimization"--