國立虎尾科技大學 |

Separable Optimization = Theory and Methods /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Separable Optimization/ by Stefan M. Stefanov.
Reminder of title:	Theory and Methods /
Author:	Stefanov, Stefan M.
Description:	XVII, 356 p. 9 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Mathematical optimization. -
Online resource:	https://doi.org/10.1007/978-3-030-78401-0
ISBN:	9783030784010

Separable Optimization = Theory and Methods /
Stefanov, Stefan M.

Separable OptimizationTheory and Methods /[electronic resource] :by Stefan M. Stefanov. - 2nd ed. 2021. - XVII, 356 p. 9 illus.online resource. - Springer Optimization and Its Applications,1771931-6836 ;. - Springer Optimization and Its Applications,104.

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.

In this book, the theory, methods and applications of separable optimization are considered. Some general results are presented, techniques of approximating the separable problem by linear programming problem, and dynamic programming are also studied. Convex separable programs subject to inequality/ equality constraint(s) and bounds on variables are also studied and convergent 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. The problems of numerical approximation of tabulated functions and numerical solution of overdetermined systems of linear algebraic equations and some systems of nonlinear equations are solved by separable convex unconstrained minimization problems. Some properties of the Knapsack polytope are also studied. This second edition includes a substantial amount of new and revised content. Three new chapters, 15-17, are included. Chapters 15-16 are devoted to the further analysis of the Knapsack problem. Chapter 17 is focused on the analysis of a nonlinear transportation problem. Three new Appendices (E-G) are also added to this edition and present technical details that help round out the coverage. Optimization problems and methods for solving the problems considered are interesting not only from the viewpoint of optimization theory, optimization methods and their applications, but also from the viewpoint of other fields of science, especially the artificial intelligence and machine learning fields within computer science. This book is intended for the researcher, practitioner, or engineer who is interested in the detailed treatment of separable programming and wants to take advantage of the latest theoretical and algorithmic results. It may also be used as a textbook for a special topics course or as a supplementary textbook for graduate courses on nonlinear and convex optimization.

ISBN: 9783030784010

Standard No.: 10.1007/978-3-030-78401-0doiSubjects--Topical Terms:

527675
Mathematical optimization.

LC Class. No.: QA402.5-402.6

Dewey Class. No.: 519.6

Separable Optimization = Theory and Methods /
LDR:05374nam a22004095i 4500 001 1057808
003 DE-He213
005 20211125232823.0
007 cr nn 008mamaa
008 220103s2021 sz | s |||| 0|eng d
020 $a 9783030784010 $9 978-3-030-78401-0
024 7 $a 10.1007/978-3-030-78401-0 $2 doi
035 $a 978-3-030-78401-0
050 4 $a QA402.5-402.6
072 7 $a PBU $2 bicssc
072 7 $a MAT003000 $2 bisacsh
072 7 $a PBU $2 thema
082 0 4 $a 519.6 $2 23
100 1 $a Stefanov, Stefan M. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1363317
245 1 0 $a Separable Optimization $h [electronic resource] : $b Theory and Methods / $c by Stefan M. Stefanov.
250 $a 2nd ed. 2021.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a XVII, 356 p. 9 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Springer Optimization and Its Applications, $x 1931-6836 ; $v 177
505 0 $a 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.
520 $a In this book, the theory, methods and applications of separable optimization are considered. Some general results are presented, techniques of approximating the separable problem by linear programming problem, and dynamic programming are also studied. Convex separable programs subject to inequality/ equality constraint(s) and bounds on variables are also studied and convergent 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. The problems of numerical approximation of tabulated functions and numerical solution of overdetermined systems of linear algebraic equations and some systems of nonlinear equations are solved by separable convex unconstrained minimization problems. Some properties of the Knapsack polytope are also studied. This second edition includes a substantial amount of new and revised content. Three new chapters, 15-17, are included. Chapters 15-16 are devoted to the further analysis of the Knapsack problem. Chapter 17 is focused on the analysis of a nonlinear transportation problem. Three new Appendices (E-G) are also added to this edition and present technical details that help round out the coverage. Optimization problems and methods for solving the problems considered are interesting not only from the viewpoint of optimization theory, optimization methods and their applications, but also from the viewpoint of other fields of science, especially the artificial intelligence and machine learning fields within computer science. This book is intended for the researcher, practitioner, or engineer who is interested in the detailed treatment of separable programming and wants to take advantage of the latest theoretical and algorithmic results. It may also be used as a textbook for a special topics course or as a supplementary textbook for graduate courses on nonlinear and convex optimization.
650 0 $a Mathematical optimization. $3 527675
650 0 $a Operations research. $3 573517
650 0 $a Management science. $3 719678
650 1 4 $a Optimization. $3 669174
650 2 4 $a Operations Research, Management Science. $3 785065
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030784003
776 0 8 $i Printed edition: $z 9783030784027
776 0 8 $i Printed edition: $z 9783030784034
830 0 $a Springer Optimization and Its Applications, $x 1931-6828 ; $v 104 $3 1255232
856 4 0 $u https://doi.org/10.1007/978-3-030-78401-0
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)