Separable Optimization
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Separable Optimization
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Author : Stefan M. Stefanov
language : en
Publisher: Springer Nature
Release Date : 2022-01-01
Separable Optimization written by Stefan M. Stefanov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-01 with Mathematics categories.
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.
Separable Programming
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Author : S.M. Stefanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Separable Programming written by S.M. Stefanov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
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.
The Solution Of Some Max Separable Optimization Problems
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Author : Amer F. Jajou
language : cs
Publisher:
Release Date : 1987
The Solution Of Some Max Separable Optimization Problems written by Amer F. Jajou and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.
Performance Of A Multifrontal Scheme For Partially Separable Optimization
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Author : University of Waterloo. Department of Computer Science
language : en
Publisher:
Release Date : 1988
Performance Of A Multifrontal Scheme For Partially Separable Optimization written by University of Waterloo. Department of Computer Science and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with categories.
Integer And Separable Programming Techniques For Large Scale Global Optimization Problems
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Author : Panayote Miltiades Pardalos
language : en
Publisher:
Release Date : 1985
Integer And Separable Programming Techniques For Large Scale Global Optimization Problems written by Panayote Miltiades Pardalos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.
Global Solutions To Factorable Nonlinear Optimization Problems Using Separable Programming Techniques
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Author : Garth P. McCormick
language : en
Publisher:
Release Date : 1985
Global Solutions To Factorable Nonlinear Optimization Problems Using Separable Programming Techniques written by Garth P. McCormick and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematical optimization categories.
Many algorithms for obtaining global solutions to nonconvex optimization problems have been proposed in recent years. The methods farthest along computationally are those for separable problems. These use linear programming codes to solve sequences of LP problems formed from piece-wise linear approximations to the nonlinear functional forms. For a large class of optimization problems, called factorable programming problems, it is possible to create equivalent separable problems. This is done at a cost: additional variables and constraints. In this paper the procedure for creating the equivalent separable problems is outlined and a brief description is given of a global solution algorithm due to Falk. A small example is given illustrating the above techniques. The example is also solved using a more direct method. Application to the solution of nonlinear least squares is illustrated with another example. Discussion of areas of research for improving the efficiency of this approach concludes the paper.
Hidden Convexity In Partially Separable Optimization
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Author : Aharon Ben-Tal
language : en
Publisher:
Release Date : 2011
Hidden Convexity In Partially Separable Optimization written by Aharon Ben-Tal and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
The paper identifies classes of nonconvex optimization problems whose convex relaxations have optimal solutions which at the same time are global optimal solutions of the original nonconvex problems. Such a hidden convexity property was so far limited to quadratically constrained quadratic problems with one or two constraints. We extend it here to problems with some partial separable structure. Among other things, the new hidden convexity results open up the possibility to solve multi-stage robust optimization problems using certain nonlinear decision rules. convex relaxation of nonconvex problems, hidden convexity, partially separable functions, robust optimization.
Incremental And Total Optimization Of Separable Functionals With Constraints
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Author : Lawrence D. Stone
language : en
Publisher:
Release Date : 1974
Incremental And Total Optimization Of Separable Functionals With Constraints written by Lawrence D. Stone and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with categories.
This paper investigates the relationship between incremental and total optimality for constrained optimization problems involving a real valued separable effectiveness functional and a vector valued separable cost functional. Existence of optimal functions is also considered.
New Duality Results For Separable Optimization Problems In Infinite Dimensions
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Author : Saba Naser Majeed
language : en
Publisher:
Release Date : 2013
New Duality Results For Separable Optimization Problems In Infinite Dimensions written by Saba Naser Majeed and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Control theory categories.
Optimization Of Industrial Systems With The Separable Programming And The Generalized Reduced Gradient Methods
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Author : Jerel L. Williams
language : en
Publisher:
Release Date : 1972
Optimization Of Industrial Systems With The Separable Programming And The Generalized Reduced Gradient Methods written by Jerel L. Williams and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with categories.