Record Nr.

UNINA9911019207003321

Autore

Berkovitz Leonard David <1924->

Titolo

Convexity and optimization in R [superscript n] / / Leonard D. Berkovitz

Pubbl/distr/stampa


New York, : J. Wiley, c2002

ISBN


9786610367009
9781280367007
1280367008
9780470311820
0470311827
9780471461661
0471461660
9780471249702
047124970X

Descrizione fisica

1 online resource (283 p.)

Collana

Pure and applied mathematicss

Disciplina

516/.08

Soggetti

Convex sets

Mathematical optimization

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references (p. 261-262) and index.

Nota di contenuto

CONVEXITY AND OPTIMIZATION IN R(n); CONTENTS; Preface; I Topics in Real Analysis; 1. Introduction; 2. Vectors in R(n); 3. Algebra of Sets; 4. Metric Topology of R(n); 5. Limits and Continuity; 6. Basic Property of Real Numbers; 7. Compactness; 8. Equivalent Norms and Cartesian Products; 9. Fundamental Existence Theorem; 10. Linear Transformations; 11. Differentiation in R(n); II Convex Sets in R(n); 1. Lines and Hyperplanes in R(n); 2. Properties of Convex Sets; 3. Separation Theorems; 4. Supporting Hyperplanes: Extreme Points; 5. Systems of Linear Inequalities: Theorems of the Alternative

6. Affine Geometry7. More on Separation and Support; III Convex Functions; 1. Definition and Elementary Properties; 2. Subgradients; 3. Differentiable Convex Functions; 4. Alternative Theorems for Convex Functions; 5. Application to Game Theory; IV Optimization Problems; 1. Introduction; 2. Differentiable Unconstrained Problems; 3. Optimization

of Convex Functions; 4. Linear Programming Problems; 5. First-Order Conditions for Differentiable Nonlinear Programming Problems; 6. Second-Order Conditions; V Convex Programming and Duality; 1. Problem Statement

2. Necessary Conditions and Sufficient Conditions3. Perturbation Theory; 4. Lagrangian Duality; 5. Geometric Interpretation; 6. Quadratic Programming; 7. Duality in Linear Programming; VI Simplex Method; 1. Introduction; 2. Extreme Points of Feasible Set; 3. Preliminaries to Simplex Method; 4. Phase II of Simplex Method; 5. Termination and Cycling; 6. Phase I of Simplex Method; 7. Revised Simplex Method; Bibliography; Index

Sommario/riassunto

A comprehensive introduction to convexity and optimization in RnThis book presents the mathematics of finite dimensional constrained optimization problems. It provides a basis for the further mathematical study of convexity, of more general optimization problems, and of numerical algorithms for the solution of finite dimensional optimization problems. For readers who do not have the requisite background in real analysis, the author provides a chapter covering this material. The text features abundant exercises and problems designed to lead the reader to a fundamental understanding of t

Record Nr.

UNIORUON00102990

Autore

DIYAB, Mahmud

Titolo

Layali al-hasad / Mahmud Diyab

Pubbl/distr/stampa


al-Qahira, : [s.n.], 1970

Descrizione fisica

159 p. ; 23 cm

Classificazione

EGI VI CAZ