An easy path to convex analysis and applications
著者
書誌事項
An easy path to convex analysis and applications
（Synthesis lectures on mathematics and statistics）（Synthesis collection of technology）
Springer, c2023
2nd ed
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注記
"1st ed Morgan & Claypool Publishers 2014"--T.p. verso
Includes bibliographical references (p. 295-296) and index
内容説明・目次
内容説明
This book examines the most fundamental parts of convex analysis and its applications to optimization and location problems. Accessible techniques of variational analysis are employed to clarify and simplify some basic proofs in convex analysis and to build a theory of generalized differentiation for convex functions and sets in finite dimensions. The book serves as a bridge for the readers who have just started using convex analysis to reach deeper topics in the field. Detailed proofs are presented for most of the results in the book and also included are many figures and exercises for better understanding the material. Applications provided include both the classical topics of convex optimization and important problems of modern convex optimization, convex geometry, and facility location.
目次
Convex Sets and Functions.- Convex Separation and Some Consequences.- Convex Generalized Differentiation.- Fenchel Conjugate and Further Topics In Subdifferentiation.- Remarkable Consequences of Convexity.- Minimal Time Functions and Related Issues.- Applications To Problems of Optimization and Equilibrium.- Applications To Location Problems.
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