Finite Dimensional Convexity and Optimization - Monique Florenzano, Cuong Le Van

Finite Dimensional Convexity and Optimization

Buch | Softcover
XII, 154 Seiten
2012 | 1. Softcover reprint of the original 1st ed. 2001
Springer Berlin (Verlag)
978-3-642-62570-1 (ISBN)
106,99 inkl. MwSt
The primary aim of this book is to present notions of convex analysis which constitute the basic underlying structure of argumentation in economic theory and which are common to optimization problems encountered in many applications. The intended readers are graduate students, and specialists of mathematical programming whose research fields are applied mathematics and economics. The text consists of a systematic development in eight chapters, with guided exercises containing sometimes significant and useful additional results. The book is appropriate as a class text, or for self-study.

1. Convexity in ?n.- 1.1 Basic concepts.- 1.2. Topological properties of convex sets.- Exercises.- 2. Separation and Polarity.- 2.1 Separation of convex sets.- 2.2 Polars of convex sets and orthogonal subspaces.- Exercises.- 3. Extremal Structure of Convex Sets.- 3.1 Extreme points and faces of convex sets.- 3.2 Application to linear inequalities. Weyl's theorem.- 3.3 Extreme points and extremal subsets of a polyhedral convex set.- Exercises.- 4. Linear Programming.- 4.1 Necessary and sufficient conditions of optimality.- 4.2 The duality theorem of linear programming.- 4.3 The simplex method.- Exercises.- 5. Convex Functions.- 5.1 Basic definitions and properties.- 5.2 Continuity theorems.- 5.3 Continuity properties of collections of convex functions.- Exercises.- 6. Differential Theory of Convex Functions.- 6.1 The Hahn-Banach dominated extension theorem.- 6.2 Sublinear functions.- 6.3 Support functions.- 6.4 Directional derivatives.- 6.5 Subgradients and subdifferential of a convex function.- 6.6 Differentiability of convex functions.- 6.7 Differential continuity for convex functions.- Exercises.- 7. Convex Optimization With Convex Constraints.- 7.1 The minimum of a convex function f: ?n ? ?.- 7.2 Kuhn-Tucker Conditions.- 7.3 Value function.- Exercises.- 8. Non Convex Optimization.- 8.1 Quasi-convex functions.- 8.2 Minimization of quasi-convex functions.- 8.3 Differentiate optimization.- Exercises.- A. Appendix.- A.1 Some preliminaries on topology.- A.2 The Mean value theorem.- A.3 The Local inversion theorem.- A.4 The implicit functions theorem.

Erscheint lt. Verlag 24.9.2012
Reihe/Serie Studies in Economic Theory
Mitarbeit Assistent: P. Gourdel
Zusatzinfo XII, 154 p.
Verlagsort Berlin
Sprache englisch
Maße 155 x 235 mm
Gewicht 272 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Angewandte Mathematik
Wirtschaft Allgemeines / Lexika
Wirtschaft Betriebswirtschaft / Management
Wirtschaft Volkswirtschaftslehre Ökonometrie
Schlagworte Convesity • Convexity • Derivative • Extrema • Game Theory • Konvexität • linear optimization • Mathematical economics • Mathematische Ökonomie • mean value theorem • Minimum • Optimierung • Optimization • Sets • Spieltheorie
ISBN-10 3-642-62570-3 / 3642625703
ISBN-13 978-3-642-62570-1 / 9783642625701
Zustand Neuware
Haben Sie eine Frage zum Produkt?
Mehr entdecken
aus dem Bereich

von Tilo Arens; Frank Hettlich; Christian Karpfinger …

Buch | Hardcover (2022)
Springer Spektrum (Verlag)
79,99