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The Mathematics of Nonlinear Programming - edition reliée, livre de poche

1988

ISBN: 0387966145

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Détails sur le livre
The Mathematics of Nonlinear Programming (Undergraduate Texts in Mathematics)

Nonlinear programming provides an excellent opportunity to explore an interesting variety of pure and solidly applicable mathematics, numerical analysis, and computing. This text develops some of the ideas and techniques involved in the optimization methods using calculus, leading to the study of convexity. This is followed by material on basic numerical methods, least squares, the Karush-Kuhn-Tucker theorem, penalty functions, and Lagrange multipliers. The authors have aimed their presentation at the student who has a working knowledge of matrix algebra and advanced calculus, but has had no previous exposure to optimization. TOC:BContents:/B Unconstrained Optimization via Calculus.- Convex Sets and Convex Functions.- Iterative Methods for Unconstrained Optimization.- Least Squares Optimization.- Convex Programming and the Karush-Kuhn-Tucker Conditions.- Penalty Methods.- Optimization with Equality Constraints.- Index.

Informations détaillées sur le livre - The Mathematics of Nonlinear Programming (Undergraduate Texts in Mathematics)


EAN (ISBN-13): 9780387966144
ISBN (ISBN-10): 0387966145
Version reliée
Livre de poche
Date de parution: 1993
Editeur: Springer
292 Pages
Poids: 0,602 kg
Langue: eng/Englisch

Livre dans la base de données depuis 2008-01-13T17:19:30+01:00 (Paris)
Page de détail modifiée en dernier sur 2024-01-20T22:54:02+01:00 (Paris)
ISBN/EAN: 9780387966144

ISBN - Autres types d'écriture:
0-387-96614-5, 978-0-387-96614-4
Autres types d'écriture et termes associés:
Auteur du livre: peress, peres, anthony, uhl, sullivan, lagrange
Titre du livre: linear programming, the mathemati, the mathematics nonlinear programming, undergraduate text


Données de l'éditeur

Auteur: Anthony L. Peressini; Francis E. Sullivan; J.J. Jr. Uhl
Titre: Undergraduate Texts in Mathematics; The Mathematics of Nonlinear Programming
Editeur: Springer; Springer US
276 Pages
Date de parution: 1988-03-02
New York; NY; US
Langue: Anglais
71,64 € (DE)
73,65 € (AT)
96,69 CHF (CH)
Available
X, 276 p.

BB; Hardcover, Softcover / Mathematik/Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik; Numerische Mathematik; Verstehen; CON_D027; Computational Mathematics and Numerical Analysis; Quantitative Economics; Wirtschaftstheorie und -philosophie; BC

1 Unconstrained Optimization via Calculus.- 1.1. Functions of One Variable.- 1.2. Functions of Several Variables.- 1.3. Positive and Negative Definite Matrices and Optimization.- 1.4. Coercive Functions and Global Minimizers.- 1.5. Eigenvalues and Positive Definite Matrices.- Exercises.- 2 Convex Sets and Convex Functions.- 2.1. Convex Sets.- 2.2. Some Illustrations of Convex Sets in Economics— Linear Production Models.- 2.3. Convex Functions.- 2.4. Convexity and the Arithmetic-Geometric Mean Inequality— An Introduction to Geometric Programming.- 2.5. Unconstrained Geometric Programming.- 2.6. Convexity and Other Inequalities.- Exercises.- 3 Iterative Methods for Unconstrained Optimization.- 3.1. Newton’s Method.- 3.2. The Method of Steepest Descent.- 3.3. Beyond Steepest Descent.- 3.4. Broyden’s Method.- 3.5. Secant Methods for Minimization.- Exercises.- 4 Least Squares Optimization.- 4.1. Least Squares Fit.- 4.2. Subspaces and Projections.- 4.3. Minimum Norm Solutions of Underdetermined Linear Systems.- 4.4. Generalized Inner Products and Norms; The Portfolio Problem.- Exercises.- 5 Convex Programming and the Karush-Kuhn-Tucker Conditions.- 5.1. Separation and Support Theorems for Convex Sets.- 5.2. Convex Programming; The Karush-Kuhn-Tucker Theorem.- 5.3. The Karush-Kuhn-Tucker Theorem and Constrained Geometric Programming.- 5.4. Dual Convex Programs.- 5.5. Trust Regions.- Exercises.- 6 Penalty Methods.- 6.1. Penalty Functions.- 6.2. The Penalty Method.- 6.3. Applications of the Penalty Function Method to Convex Programs.- Exercises.- 7 Optimization with Equality Constraints.- 7.1. Surfaces and Their Tangent Planes.- 7.2. Lagrange Multipliers and the Karush-Kuhn-Tucker Theorem for Mixed Constraints.- 7.3. Quadratic Programming.- Exercises.

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