Author | Stefanov, Stefan M. author |
---|---|
Title | Separable Programming [electronic resource] : Theory and Methods / by Stefan M. Stefanov |
Imprint | Boston, MA : Springer US : Imprint: Springer, 2001 |
Connect to | http://dx.doi.org/10.1007/978-1-4757-3417-1 |
Descript | XIX, 314 p. online resource |
1 Preliminaries: Convex Analysis and Convex Programming -- One โ Separable Programming -- 2 Introduction. Approximating the Separable Problem -- 3 Convex Separable Programming -- 4 Separable Programming: A Dynamic Programming Approach -- Two โ 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 โ?โ -- 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 โ 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 โ Some Definitions and Theorems from Calculus -- B Appendix B โ Metric, Banach and Hilbert Spaces -- C Appendix C โ Existence of Solutions to Optimization Problems โ A General Approach -- D Appendix D โ Best Approximation: Existence and Uniqueness -- Bibliography, Index, Notation, List of Statements -- Notation -- List of Statements