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Nonlinear Programming: Analysis and Methodsby Mordecai Avriel
Synopses & Reviews
Comprehensive and complete, this overview provides a single-volume treatment of key algorithms and theories. The author provides clear explanations of all theoretical aspects, with rigorous proof of most results. The two-part treatment begins with the derivation of optimality conditions and discussions of convex programming, duality, generalized convexity, and analysis of selected nonlinear programs. The second part concerns techniques for numerical solutions and unconstrained optimization methods, and it presents commonly used algorithms for constrained nonlinear optimization problems. This graduate-level text requires no advanced mathematical background beyond elementary calculus, linear algebra, and real analysis. 1976 edition. 58 figures. 7 tables.
Book News Annotation:
<:st> This graduate textbook derives the theory of convex sets and functions, convex programming, nonlinear convex duality, and generalized convexity, then introduces numerical solution techniques for nonlinear optimization problems. The Dover edition is an unabridged reprint of the work originally published by Prentice Hall in 1976 and cited in
Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)
This text provides an excellent bridge between principal theories and concepts and their practical implementation. Topics include convex programming, duality, generalized convexity, analysis of selected nonlinear programs, techniques for numerical solutions, and unconstrained optimization methods.
This overview provides a single-volume treatment of key algorithms and theories. Begins with the derivation of optimality conditions and discussions of convex programming, duality, generalized convexity, and analysis of selected nonlinear programs, and then explores techniques for numerical solutions and unconstrained optimization methods. 1976 edition. Includes 58 figures and 7 tables.
An excellent bridge between principal theories and concepts and their practical implementation, this graduate-level text is a major work by a leading figure in the field of operations research. Unabridged republication of the edition published by Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1976.
Table of Contents
Author's Preface to the Dover Edition
2. Classical Optimization--Unconstrained and Equality Constrained Problems
3. Optimality Conditions for Constrained Extrema
4. Convex Sets and Functions
5. Duality in Nonlinear Convex Programming
6. Generalized Convexity
7. Analysis of Selected Nonlinear Programming Problems
8. One-Dimensional Optimization
9. Multidimensional Unconstrained Optimization Without Derivatives: Empirical and Conjugate Direction Methods
10. Second Derivative, Steepest Descent and Conjugate Gradient Methods
11. Variable Metric Algorithms
12. Penalty Function Methods
13. Solution of Constrained Problems by Extensions of Unconstrained Optimization Techniques
14. Approximation-Type Algorithms
Author Index. Subject Index.
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