Convex Analysis and Minimization Algorithms I: Fundamentals / Edition 1

Convex Analysis and Minimization Algorithms I: Fundamentals / Edition 1

by Jean-Baptiste Hiriart-Urruty, Claude Lemarechal
     
 

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ISBN-10: 3540568506

ISBN-13: 9783540568506

Pub. Date: 10/30/1996

Publisher: Springer Berlin Heidelberg

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.

Overview

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.

Product Details

ISBN-13:
9783540568506
Publisher:
Springer Berlin Heidelberg
Publication date:
10/30/1996
Series:
Grundlehren der mathematischen Wissenschaften Series, #305
Edition description:
1st ed. 1993. 2nd corr. printing 1996
Pages:
418
Product dimensions:
1.06(w) x 6.14(h) x 9.21(d)

Table of Contents

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.

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