Projected Lagrangian Algorithms for Nonlinear Minimax and L1 Optimization PDF Download
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Author: Michael Lockhart Overton
Publisher:
ISBN:
Category : Algorithms
Languages : en
Pages : 360
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Book Description
Author: Michael Lockhart Overton
Publisher:
ISBN:
Category : Algorithms
Languages : en
Pages : 360
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Book Description
Author: M. L. Overton
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Stanford University. Systems Optimization Laboratory
Publisher:
ISBN:
Category :
Languages : en
Pages : 50
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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
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Author: Walter Murray
Publisher:
ISBN:
Category :
Languages : en
Pages : 40
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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: Ernesto G. Birgin
Publisher: SIAM
ISBN: 1611973368
Category : Mathematics
Languages : en
Pages : 222
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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.
Author: Stanford University. Systems Optimization Laboratory
Publisher:
ISBN:
Category :
Languages : en
Pages : 82
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Book Description
This report contains a complete derivation and description of two algorithms for nonlinearly constrained optimization which are based on properties of the solution trajectory of the quadratic penalty function and the logarithmic barrier function. The methods utilize the penalty and barrier functions only as merit functions, and do not generate iterates by solving a sequence of ill-conditioned problems. The search direction is the solution of a simple, well-posed quadratic program (QP), where the quadratic objective function is an approximation to the Lagrangian function; the steplength is based on a sufficient decrease in a penalty or barrier function, to ensure progress toward the solution. The penalty trajectory algorithm was first proposed by Murray in 1969; the barrier trajectory algorithm, which retains feasibility throughout, was given by Wright in 1976. Here we give a unified presentation of both algorithms, and indicate their relationship to other QP-based methods. Full details of implementation are included, as well as numerical results that display the success of the methods on non-trivial problems. (Author).
Author: Bruce A. Murtagh
Publisher:
ISBN:
Category : Nonlinear programming
Languages : en
Pages : 55
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Author: M. A. Diniz-Ehrhardt
Publisher:
ISBN:
Category :
Languages : en
Pages : 21
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Author: Justin Solomon
Publisher: CRC Press
ISBN: 1482251892
Category : Computers
Languages : en
Pages : 400
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Book Description
Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig
