Separable Optimization

Stefan M. Stefanov is a Professor in the Department of Mathematics, South-West University "Neofit Rilski," Blagoevgrad, Bulgaria. He is author of several books, and journal and conference papers. His interests are in the areas of optimization (separable, convex, stochastic, nondifferentiable, nonlinear), operations research, numerical analysis, approximation theory, inequalities.

• 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.