Separable Programming

1 Preliminaries: Convex Analysis and Convex Programming.- One — Separable Programming.- 2 Introduction. Approximating the Separable Problem.- 3 Convex Separable Programming.- 4 Separable Programming: A Dynamic Programming Approach.- Two — Convex Separable Programming With Bounds On The Variables.- Statement of the Main Problem. Basic Result.- Version One: Linear Equality Constraints.- 7 The Algorithms.- 8 Version Two: Linear Constraint of the Form “?”.- 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.- Three — Selected Supplementary Topics and Applications.- 12 Approximations with Respect to ?1 and ??-Norms: An Application of Convex Separable Unconstrained Nondifferentiable Optimization.- 13 About Projections in the Implementation of Stochastic Quasigradient Methods to Some Probabilistic Inventory Control Problems. The Stochastic Problem of Best Chebyshev Approximation.- 14 Integrality of the Knapsack Polytope.- Appendices.- A Appendix A — Some Definitions and Theorems from Calculus.- B Appendix B — Metric, Banach and Hilbert Spaces.- C Appendix C — Existence of Solutions to Optimization Problems — A General Approach.- D Appendix D — Best Approximation: Existence and Uniqueness.- Bibliography, Index, Notation, List of Statements.- Notation.- List of Statements.