Separable Programming: Theory and Methods / Edition 1

Separable Programming: Theory and Methods / Edition 1

by S.M. Stefanov
     
 

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ISBN-10: 1441948511

ISBN-13: 9781441948519

Pub. Date: 12/06/2010

Publisher: Springer US

In this book, the author considers separable programming and, in particular, one of its important cases - convex separable programming. Some general results are presented, techniques of approximating the separable problem by linear programming and dynamic programming are considered.
Convex separable programs subject to inequality/ equality constraint(s) and

Overview

In this book, the author considers separable programming and, in particular, one of its important cases - convex separable programming. Some general results are presented, techniques of approximating the separable problem by linear programming and dynamic programming are considered.
Convex separable programs subject to inequality/ equality constraint(s) and bounds on variables are also studied and iterative algorithms of polynomial complexity are proposed.
As an application, these algorithms are used in the implementation of shastic quasigradient methods to some separable shastic programs. Numerical approximation with respect to I1 and I4 norms, as a convex separable nonsmooth unconstrained minimization problem, is considered as well.
Audience: Advanced undergraduate and graduate students, mathematical programming/ operations research specialists.

Product Details

ISBN-13:
9781441948519
Publisher:
Springer US
Publication date:
12/06/2010
Series:
Applied Optimization Series, #53
Edition description:
Softcover reprint of hardcover 1st ed. 2001
Pages:
314
Product dimensions:
0.71(w) x 9.21(h) x 6.14(d)

Table of Contents

List of Figures. List of Tables. Preface. 1. Preliminaries: Convex Analysis and Convex Programming. Part One: Separable Programming. 2. Introduction. Approximating the Separable Problem. 3. Convex Separable Programming. 4. Separable Programming: A Dynamic Programming Approach. Part Two: 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 '>='. 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 Three: Selected Supplementary Topics and Applications. 12. Approximations with Respect to l1- and lINFINITY-Norms: An Application of Convex Separable Unconstrained Nondifferentiable Optimization. 13. About Projections in the Implementation of Shastic Quasigradient Methods to Some Probabilistic Inventory Control Problems. The Shastic Problem of Best Chebyshev Approximation. 14. Integrality of the Knapsack Polytope. Appendices. Bibliography. Index. Notation. List of Statements.

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