Nonlinear programming theory and algorithms
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 constra...
| Otros Autores: | , |
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| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Hoboken, N.J. :
Wiley-Interscience
c2006.
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| Edición: | 3rd ed |
| Colección: | Wiley-Interscience
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| Materias: | |
| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009665108806719 |
Tabla de Contenidos:
- 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
- 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
- 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
- Exercises
