Nonlinear programming : theory and algorithms

Includes Bibliography and Index

4.4. Second-Order Necessary and Sufficient Optimality Conditions for Constrained Problems. Ch. 5. Constraint Qualifications. 5.1. The Cone of Tangents. 5.2. Other Constraint Qualifications. 5.3. Problems with Inequality and Equality Constraints. Ch. 6. Lagrangian Duality and Saddle Point Optimality Conditions. 6.1. The 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 Programs --
pt. 3. Algorithms and Their Convergence. Ch. 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. Ch. 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 Derivatives. 8.7. 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. Ch. 9. Penalty and Barrier Functions. 9.1. The 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. A Polynomial-Time Algorithm for Linear Programming Based on a Barrier Function. Ch. 10. Methods of Feasible Directions. 10.1. The Method of Zoutendijk. 10.2. Convergence Analysis of the Method of Zoutendijk. 10.3. Successive Linear Programming Approach. 10.4. Successive Quadratic Programming or Projected Lagrangian Approach. 10.5. The Gradient Projection Method of Rosen. 10.6. The Method of Reduced Gradient of Wolfe and the Generalized Reduced Gradient Method. 10.7. The Convex-Simplex Method of Zangwill. 10.8. Effective First- and Second-Order Variants of the Reduced Gradient Method. Ch. 11. Linear Complementary Problem, and Quadratic, Separable, Fractional, and Geometric Programming. 11.1. The Linear Complementary Problem. 11.2. Quadratic Programming. 11.3. Separable Programming. 11.4. Linear Fractional Programming. 11.5. Geometric Programming --
Appendix A. Mathematical Review --
Appendix B. Summary of Convexity, Optimality Conditions, and Duality.

This updated textbook offers an overview of convex analysis, the foundations of optimization and computational methods. It emphasizes the implementation of numerical methods and focuses on the concept of error and the need to analyze and predict it.