Separable Optimization

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.