An Algorithm for Separable Convex Programming Under Linear Equality Constraints PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download An Algorithm for Separable Convex Programming Under Linear Equality Constraints PDF full book. Access full book title An Algorithm for Separable Convex Programming Under Linear Equality Constraints by James E. FALK. Download full books in PDF and EPUB format.
Author: James E. FALK
Publisher:
ISBN:
Category :
Languages : en
Pages : 23
Get Book Here
Book Description
Author: James E. FALK
Publisher:
ISBN:
Category :
Languages : en
Pages : 23
Get Book Here
Book Description
Author: S.M. Stefanov
Publisher: Springer Science & Business Media
ISBN: 1475734174
Category : Mathematics
Languages : en
Pages : 323
Get Book Here
Book Description
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.
Author: James Edward Falk
Publisher:
ISBN:
Category : Convex programming
Languages : en
Pages : 17
Get Book Here
Book Description
Author: Agha Iqbal Ali
Publisher:
ISBN:
Category : Convex programming
Languages : en
Pages : 22
Get Book Here
Book Description
Document discusses a new algorithm for the separable convex programming with linear constraints. This is based on the approximation of the objective function by at most two linear pieces in the neighborhood of the current feasible solution. The two segments will be adaptively defined rather than predecided fixed grids. If, furthermore, the objective function is differentiable, and one introduces a non-Archimedean infinitesimal, the algorithm generates a sequence of feasible solutions every cluster point of which is an optimal solution. Computational tests on the problem with up to 196 non-linear variables is presented. (Author).
Author: Stefan M. Stefanov
Publisher: Springer Nature
ISBN: 3030784010
Category : Mathematics
Languages : en
Pages : 360
Get Book Here
Book Description
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.
Author: Stephen P. Boyd
Publisher: Cambridge University Press
ISBN: 9780521833783
Category : Business & Economics
Languages : en
Pages : 744
Get Book Here
Book Description
Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.
Author: Dimitri P. Bertsekas
Publisher: Academic Press
ISBN: 148326047X
Category : Mathematics
Languages : en
Pages : 412
Get Book Here
Book Description
Computer Science and Applied Mathematics: Constrained Optimization and Lagrange Multiplier Methods focuses on the advancements in the applications of the Lagrange multiplier methods for constrained minimization. The publication first offers information on the method of multipliers for equality constrained problems and the method of multipliers for inequality constrained and nondifferentiable optimization problems. Discussions focus on approximation procedures for nondifferentiable and ill-conditioned optimization problems; asymptotically exact minimization in the methods of multipliers; duality framework for the method of multipliers; and the quadratic penalty function method. The text then examines exact penalty methods, including nondifferentiable exact penalty functions; linearization algorithms based on nondifferentiable exact penalty functions; differentiable exact penalty functions; and local and global convergence of Lagrangian methods. The book ponders on the nonquadratic penalty functions of convex programming. Topics include large scale separable integer programming problems and the exponential method of multipliers; classes of penalty functions and corresponding methods of multipliers; and convergence analysis of multiplier methods. The text is a valuable reference for mathematicians and researchers interested in the Lagrange multiplier methods.
Author: Jorge Nocedal
Publisher: Springer Science & Business Media
ISBN: 0387227423
Category : Mathematics
Languages : en
Pages : 651
Get Book Here
Book Description
The new edition of this book presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on methods best suited to practical problems. This edition has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are widely used in practice and are the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience.
Author: Nainan Kovoor
Publisher:
ISBN:
Category : Algorithms
Languages : en
Pages : 7
Get Book Here
Book Description
Abstract: "We consider the problem of minimizing a separable differentiable strictly convex function on R[superscript n] subject to m equality constraints and upper and lower bounds (box constraints). We provide a parametric characterization in R[superscript m] of the family of solutions to this problem, thereby showing equivalence with a problem of search in an arrangement of hyperplanes in R[superscript m]. For the special case of the euclidean distance function and m = 2, we obtain a strongly polynomial algorithm running in time [theta](n2).
Author: Yurii Nesterov
Publisher: SIAM
ISBN: 9781611970791
Category : Mathematics
Languages : en
Pages : 414
Get Book Here
Book Description
Specialists working in the areas of optimization, mathematical programming, or control theory will find this book invaluable for studying interior-point methods for linear and quadratic programming, polynomial-time methods for nonlinear convex programming, and efficient computational methods for control problems and variational inequalities. A background in linear algebra and mathematical programming is necessary to understand the book. The detailed proofs and lack of "numerical examples" might suggest that the book is of limited value to the reader interested in the practical aspects of convex optimization, but nothing could be further from the truth. An entire chapter is devoted to potential reduction methods precisely because of their great efficiency in practice.
