Projected Lagrangian Algorithms for Nonlinear Minimax and L1 Optimization 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 Projected Lagrangian Algorithms for Nonlinear Minimax and L1 Optimization PDF full book. Access full book title Projected Lagrangian Algorithms for Nonlinear Minimax and L1 Optimization by Michael Lockhart Overton. Download full books in PDF and EPUB format.
Author: Michael Lockhart Overton
Publisher:
ISBN:
Category : Algorithms
Languages : en
Pages : 360
Get Book Here
Book Description
Author: Michael Lockhart Overton
Publisher:
ISBN:
Category : Algorithms
Languages : en
Pages : 360
Get Book Here
Book Description
![Projected Lagangian [i.e. Lagrangian] Algorithms for Nonlinear Minimax and L1 Optimization PDF](https://books.google.com/books/content/images/frontcover/6SGUGwAACAAJ?fife=w80-h100)
Author: Stanford University. Computer Science Department
Publisher:
ISBN:
Category : Algorithms
Languages : en
Pages : 164
Get Book Here
Book Description
Author: Walter Murray
Publisher:
ISBN:
Category :
Languages : en
Pages : 82
Get Book Here
Book Description
The minimax problem is an unconstrained optimization problem whose objective functions is not differentiable everywhere, and hence cannot be solved efficiently by standard techniques for unconstrained optimization. It is well known that the problem can be transformed into a nonlinearly constrained optimization problem with one extra variable, where the objective and constraint functions are continuously differentiable. This equivalent problem has special properties which are ignored if solved by a general-purpose constrained optimization method. The algorithm we present exploits the special structure of the equivalent problem. A direction of search is obtained at each iteration of the algorithm by solving a equality-constrained quadratic programming problem, related to one a projected Lagrangian method might use to solve the equivalent constrained optimization problem. Special Lagrangian multiplier estimates are used to form an approximation to the Hessian of the Lagrangian function, which appears in the quadratic program. Analytical Hessians, finite-differencing or quasi-Newton updating may be used in the approximation of this matrix. The resulting direction of search is guaranteed to be a descent direction for the minimax objective function. Under mild conditions the algorithms are locally quadratically convergent if analytical Hessians are used. (Author).
Author: Stanford University. Systems Optimization Laboratory
Publisher:
ISBN:
Category :
Languages : en
Pages : 50
Get Book Here
Book Description
Author: M. L. Overton
Publisher:
ISBN:
Category :
Languages : en
Pages :
Get Book Here
Book Description
Author: Walter Murray
Publisher:
ISBN:
Category :
Languages : en
Pages : 40
Get Book Here
Book Description
The nonlinear l (sub 1) problem is an unconstrained optimization problem whose objective function is not differentiable everywhere, and hence cannot be solved efficiently using standard techniques for unconstrained optimization. The problem can be transformed into a nonlinearly constrained optimization problem, but it involves many extra variables. We show how to construct a method based on projected Lagrangian methods for constrained optimization which requires successively solving quadratic programs in the same number of variables as that of the original problem. Special Lagrange multiplier estimates are used to form an approximation to the Hessian of the Lagrangian function, which appears in the quadratic program. A special line search algorithm is used to obtain a reduction in the l (sub 1) objective function at each iteration. Under mild conditions the method is locally quadratically convergent if analytical Hessians are used. (Author).
Author: Rene Gonin
Publisher: Routledge
ISBN: 1351428179
Category : Mathematics
Languages : en
Pages : 318
Get Book Here
Book Description
Complete with valuable FORTRAN programs that help solve nondifferentiable nonlinear LtandLo.-norm estimation problems, this important reference/text extensively delineates ahistory of Lp-norm estimation. It examines the nonlinear Lp-norm estimation problem that isa viable alternative to least squares estimation problems where the underlying errordistribution is nonnormal, i.e., non-Gaussian.Nonlinear LrNorm Estimation addresses both computational and statistical aspects ofLp-norm estimation problems to bridge the gap between these two fields . . . contains 70useful illustrations ... discusses linear Lp-norm as well as nonlinear Lt, Lo., and Lp-normestimation problems . . . provides all appropriate computational algorithms and FORTRANlistings for nonlinear Lt- and Lo.-norm estimation problems . . . guides readers with clear endof-chapter notes on related topics and outstanding research publications . . . contains numericalexamples plus several practical problems .. . and shows how the data can prescribe variousapplications of Lp-norm alternatives.Nonlinear Lp-Norm Estimation is an indispensable reference for statisticians,operations researchers, numerical analysts, applied mathematicians, biometricians, andcomputer scientists, as well as a text for graduate students in statistics or computer science.
Author: J. E. Dennis, Jr.
Publisher: SIAM
ISBN: 9781611971200
Category : Mathematics
Languages : en
Pages : 394
Get Book Here
Book Description
This book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms covered are all based on Newton's method or "quasi-Newton" methods, and the heart of the book is the material on computational methods for multidimensional unconstrained optimization and nonlinear equation problems. The republication of this book by SIAM is driven by a continuing demand for specific and sound advice on how to solve real problems. The level of presentation is consistent throughout, with a good mix of examples and theory, making it a valuable text at both the graduate and undergraduate level. It has been praised as excellent for courses with approximately the same name as the book title and would also be useful as a supplemental text for a nonlinear programming or a numerical analysis course. Many exercises are provided to illustrate and develop the ideas in the text. A large appendix provides a mechanism for class projects and a reference for readers who want the details of the algorithms. Practitioners may use this book for self-study and reference. For complete understanding, readers should have a background in calculus and linear algebra. The book does contain background material in multivariable calculus and numerical linear algebra.
Author: Wenyu Sun
Publisher: Springer Science & Business Media
ISBN: 0387249761
Category : Mathematics
Languages : en
Pages : 689
Get Book Here
Book Description
Optimization Theory and Methods can be used as a textbook for an optimization course for graduates and senior undergraduates. It is the result of the author's teaching and research over the past decade. It describes optimization theory and several powerful methods. For most methods, the book discusses an idea’s motivation, studies the derivation, establishes the global and local convergence, describes algorithmic steps, and discusses the numerical performance.
Author: Ernesto G. Birgin
Publisher: SIAM
ISBN: 1611973368
Category : Mathematics
Languages : en
Pages : 222
Get Book Here
Book Description
This book focuses on Augmented Lagrangian techniques for solving practical constrained optimization problems. The authors: rigorously delineate mathematical convergence theory based on sequential optimality conditions and novel constraint qualifications; orient the book to practitioners by giving priority to results that provide insight on the practical behavior of algorithms and by providing geometrical and algorithmic interpretations of every mathematical result; and fully describe a freely available computational package for constrained optimization and illustrate its usefulness with applications.
