Nonlinear programming : theory and algorithms

Mokhtar S. Bazaraa, Hanif D. Sherali, C.M. Shetty
Bok · Engelsk · 2006 Mokhtar S.. Bazaraa,· Electronic books.

Annen tittel	Nonlinear Programming: Theory and Algorithms, Third Edition
Medvirkende	Sherali, Hanif D.. Shetty, C.M..
Utgitt	Hoboken, N.J. : Wiley-Interscience , cop. 2006
Omfang	XV, 853 s. : ill.
Utgave	3rd ed.
Opplysninger	Description based upon print version of record.. - NONLINEAR PROGRAMMING Theory and Algorithms; Contents; Chapter 1 Introduction; 1.1 Problem Statement and Basic Definitions; 1.2 Illustrative Examples; 1.3 Guidelines for Model Construction; Exercises; Notes and References; Part 1 Convex Analysis; Chapter 2 Convex Sets; 2.1 Convex Hulls; 2.2 Closure and Interior of a Set; 2.3 Weierstrass's Theorem; 2.4 Separation and Support of Sets; 2.5 Convex Cones and Polarity; 2.6 Polyhedral Sets, Extreme Points, and Extreme Directions; 2.7 Linear Programming and the Simplex Method; Exercises; Notes and References. - 4.4 Second-Order Necessary and Sufficient Optimality Conditions for Constrained ProblemsExercises; Notes and References; Chapter 5 Constraint Qualifications; 5.1 Cone of Tangents; 5.2 Other Constraint Qualifications; 5.3 Problems Having Inequality and Equality Constraints; Exercises; Notes and References; Chapter 6 Lagrangian Duality and Saddle Point Optimality Conditions; 6.1 Lagrangian Dual Problem; 6.2 Duality Theorems and Saddle Point Optimality Conditions; 6.3 Properties of the Dual Function; 6.4 Formulating and Solving the Dual Problem; 6.5 Getting the Primal Solution. - 6.6 Linear and Quadratic ProgramsExercises; Notes and References; Part 3 Algorithms and Their Convergence; Chapter 7 The Concept of an Algorithm; 7.1 Algorithms and Algorithmic Maps; 7.2 Closed Maps and Convergence; 7.3 Composition of Mappings; 7.4 Comparison Among Algorithms; Exercises; Notes and References; Chapter 8 Unconstrained Optimization; 8.1 Line Search Without Using Derivatives; 8.2 Line Search Using Derivatives; 8.3 Some Practical Line Search Methods; 8.4 Closedness of the Line Search Algorithmic Map; 8.5 Multidimensional Search Without Using Derivatives. - 8.6 Multidimensional Search Using Derivatives8.7 Modification of Newton's Method: Levenberg-Marquardt and Trust Region Methods; 8.8 Methods Using Conjugate Directions: Quasi-Newton and Conjugate Gradient Methods; 8.9 Subgradient Optimization Methods; Exercises; Notes and References; Chapter 9 Penalty and Barrier Functions; 9.1 Concept of Penalty Functions; 9.2 Exterior Penalty Function Methods; 9.3 Exact Absolute Value and Augmented Lagrangian Penalty Methods; 9.4 Barrier Function Methods; 9.5 Polynomial-Time Interior Point Algorithms for Linear Programming Based on a Barrier Function. - Chapter 3 Convex Functions and Generalizations3.1 Definitions and Basic Properties; 3.2 Subgradients of Convex Functions; 3.3 Differentiable Convex Functions; 3.4 Minima and Maxima of Convex Functions; 3.5 Generalizations of Convex Functions; Exercises; Notes and References; Part 2 Optimality Conditions and Duality; Chapter 4 The Fritz John and Karush-Kuhn-Tucker Optimality Conditions; 4.1 Unconstrained Problems; 4.2 Problems Having Inequality Constraints; 4.3 Problems Having Inequality and Equality Constraints. - Exercises. - COMPREHENSIVE COVERAGE OF NONLINEAR PROGRAMMING THEORY AND ALGORITHMS, THOROUGHLY REVISED AND EXPANDED Nonlinear Programming: Theory and Algorithms-now in an extensively updated Third Edition-addresses the problem of optimizing an objective function in the presence of equality and inequality constraints. Many realistic problems cannot be adequately represented as a linear program owing to the nature of the nonlinearity of the objective function and/or the nonlinearity of any constraints. The Third Edition begins with a general introduction to nonlinear programming with i
Emner	Nonlinear programming Civil & Environmental Engineering Engineering & Applied Sciences Ikke-lineær programmering Vis mer... Operations Research Optimering ikke-lineær programmering
Sjanger	Electronic books.
Dewey	519.7/6 . - 519.7
ISBN	0471486000. - 9780471486008