Convex Analysis and Minimization Algorithms I: Fundamentals

ISBN-13: 9783642081613 / Angielski / Miękka / 2011 / 418 str.

Jean-Baptiste Hiriart-Urruty;Claude Lemarechal

Opis

This book covers the fundamentals of convex analysis, a refinement of standard calculus with equalities and approximations replaced by inequalities. Reviews minimization algorithms, which provide immediate application to optimization and operations research.

Recenzje

From the reviews: "... The book is very well written, nicely illustrated, and clearly understandable even for senior undergraduate students of mathematics... Throughout the book, the authors carefully follow the recommendation by A. Einstein: 'Everything should be made as simple as possible, but not simpler.'"

Spis treści

Table of Contents Part I.- I. Convex Functions of One Real Variable.- II. Introduction to Optimization Algorithms.- III. Convex Sets.- IV. Convex Functions of Several Variables.- V. Sublinearity and Support Functions.- VI. Subdifferentials of Finite Convex Functions.- VII. Constrained Convex Minimization Problems: Minimality Conditions, Elements of Duality Theory.- VIII. Descent Theory for Convex Minimization: The Case of Complete Information.- Appendix: Notations.- 1 Some Facts About Optimization.- 2 The Set of Extended Real Numbers.- 3 Linear and Bilinear Algebra.- 4 Differentiation in a Euclidean Space.- 5 Set-Valued Analysis.- 6 A Bird’s Eye View of Measure Theory and Integration.- Bibliographical Comments.- References.