Applied Optimization

Theory and Methods

By: S.M. Stefanov

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Hardcover | 31 May 2001

At a Glance

Hardcover
340 Pages

Dimensions(cm)
25.4 x 17.15 x 2.54

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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 stochastic quasigradient methods to some separable stochastic 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.

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Non-Fiction Mathematics Optimisation Linear Programming Applied Mathematics Computing & I.T.Computer Programming & Software Development Engineering & Technology Mechanical Engineering & Materials Production & Industrial Engineering

List of Figures
List of Tables
Preface
Preliminaries: Convex Analysis and Convex Programming	p. 1
Separable Programming	p. 63
Introduction. Approximating the Separable Problem	p. 65
Convex Separable Programming	p. 79
Separable Programming: A Dynamic Programming Approach	p. 91
Convex Separable Programming with Bounds on the Variables	p. 141
Statement of the Main Problem. Basic Result	p. 143
Version One: Linear Equality Constraints	p. 151
The Algorithms	p. 159
Version Two: Linear Constraint of the Form "[greater than or equal to]"	p. 175
Well-Posedness of Optimization Problems. On the Stability of the Set of Saddle Points of the Lagrangian	p. 181
Extensions	p. 195
Applications and Computational Experiments	p. 207
Selected Supplementary Topics and Applications	p. 227
Approximation with Respect to l[subscript 1]- and l[subscript [infinity]]- Norms: An Application of Convex Separable Unconstrained Nondifferentiable Optimization	p. 229
About Projections in the Implementation of Stochastic Quasigradient Methods to Some Probabilistic Inventory Control Problems. The Stochastic Problem of Best Chebyshev Approximation	p. 251
Integrality of the Knapsack Polytope	p. 263
Some Definitions and Theorems from Calculus	p. 271
Metric, Banach and Hilbert Spaces	p. 275
Existence of Solutions to Optimization Problems - A General Approach	p. 279
Best Approximation: Existence and Uniqueness	p. 285
Bibliography, Index, Notation, List of Statements	p. 289
Bibliography	p. 291
Index	p. 301
Notation	p. 305
List of Statements	p. 309
Table of Contents provided by Blackwell. All Rights Reserved.

Applied Optimization

Theory and Methods

At a Glance

New Edition

Hardcover

Shipping

How to return your order

Defective items

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