凸解析と応用への平易な道（第２版） An Easy Path to Convex Analysis and Applications (Synthesis Lectures on Mathematics & Statistics) （2ND）

Mordukhovich, Boris/ Nam, Nguyen Mau

Springer International Publishing AG（2023/05発売）

• 製本 Hardcover:ハードカバー版／ページ数 300 p.
• 商品コード 9783031264573

Full Description

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.

Contents

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.