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Table of Contents
Preface to the New Edition
Preface.-1 Preliminaries: Convex Analysis and Convex Programming
Part I. Separable Programming
2 Introduction: Approximating the Separable Problem
3. Convex Separable Programming
4. Separable Programming: A Dynamic Programming Approach
Part II. Convex Separable Programming With Bounds on the Variables
5. Statement of the Main Problem. Basic Result
6. Version One: Linear Equality Constraints
7. The Algorithms
8. Version Two: Linear Constraint of the Form \geq
9. Well-Posedness of Optimization Problems. On the Stability of the Set of Saddle Points of the Lagrangian
10. Extensions
11. Applications and Computational Experiments
Part III. Selected Supplementary Topics and Applications
12. Applications of Convex Separable Unconstrained Nondifferentiable Optimization to Approximation Theory
13. About Projections in the Implementation of Stochastic Quasigradient Methods to Some Probabilistic Inventory Control Problems
14. Valid Inequalities, Cutting Planes and Integrality ofthe Knapsack Polytope
15. Relaxation of the Equality Constrained Convex Continuous Knapsack Problem
16. On the Solution of Multidimensional Convex Separable Continuous Knapsack Problem with Bounded Variables
17. Characterization of the Optimal Solution of the Convex Generalized Nonlinear Transportation Problem
Appendices
A. Some Definitions and Theorems from Calculus
B. Metric, Banach and Hilbert Spaces
C. Existence of Solutions to Optimization Problems : A General Approach
D. Best Approximation: Existence and Uniqueness
E. On the Solvability of a Quadratic Optimization Problem with a Feasible Region Defined as a Minkowski Sum of a Compact Set and Finitely Generated Convex Closed Cone- F. On the Cauchy-Schwarz Inequality Approach for Solving a Quadratic Optimization Problem
G. Theorems of the Alternative
Bibliography
List of Notation
List of Statements
Index.
Preface.-1 Preliminaries: Convex Analysis and Convex Programming
Part I. Separable Programming
2 Introduction: Approximating the Separable Problem
3. Convex Separable Programming
4. Separable Programming: A Dynamic Programming Approach
Part II. Convex Separable Programming With Bounds on the Variables
5. Statement of the Main Problem. Basic Result
6. Version One: Linear Equality Constraints
7. The Algorithms
8. Version Two: Linear Constraint of the Form \geq
9. Well-Posedness of Optimization Problems. On the Stability of the Set of Saddle Points of the Lagrangian
10. Extensions
11. Applications and Computational Experiments
Part III. Selected Supplementary Topics and Applications
12. Applications of Convex Separable Unconstrained Nondifferentiable Optimization to Approximation Theory
13. About Projections in the Implementation of Stochastic Quasigradient Methods to Some Probabilistic Inventory Control Problems
14. Valid Inequalities, Cutting Planes and Integrality ofthe Knapsack Polytope
15. Relaxation of the Equality Constrained Convex Continuous Knapsack Problem
16. On the Solution of Multidimensional Convex Separable Continuous Knapsack Problem with Bounded Variables
17. Characterization of the Optimal Solution of the Convex Generalized Nonlinear Transportation Problem
Appendices
A. Some Definitions and Theorems from Calculus
B. Metric, Banach and Hilbert Spaces
C. Existence of Solutions to Optimization Problems : A General Approach
D. Best Approximation: Existence and Uniqueness
E. On the Solvability of a Quadratic Optimization Problem with a Feasible Region Defined as a Minkowski Sum of a Compact Set and Finitely Generated Convex Closed Cone- F. On the Cauchy-Schwarz Inequality Approach for Solving a Quadratic Optimization Problem
G. Theorems of the Alternative
Bibliography
List of Notation
List of Statements
Index.