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Newton-Type Methods for Optimization and Variational Problems

2014-07-08 Business & Economics
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Release : 2014-07-08
Genre : Business & Economics
Kind : eBook
Book Rating : 475/5 ( reviews)

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Book Synopsis Newton-Type Methods for Optimization and Variational Problems by : Alexey F. Izmailov

Download or read book Newton-Type Methods for Optimization and Variational Problems written by Alexey F. Izmailov. This book was released on 2014-07-08. Available in PDF, EPUB and Kindle. Book excerpt: This book presents comprehensive state-of-the-art theoretical analysis of the fundamental Newtonian and Newtonian-related approaches to solving optimization and variational problems. A central focus is the relationship between the basic Newton scheme for a given problem and algorithms that also enjoy fast local convergence. The authors develop general perturbed Newtonian frameworks that preserve fast convergence and consider specific algorithms as particular cases within those frameworks, i.e., as perturbations of the associated basic Newton iterations. This approach yields a set of tools for the unified treatment of various algorithms, including some not of the Newton type per se. Among the new subjects addressed is the class of degenerate problems. In particular, the phenomenon of attraction of Newton iterates to critical Lagrange multipliers and its consequences as well as stabilized Newton methods for variational problems and stabilized sequential quadratic programming for optimization. This volume will be useful to researchers and graduate students in the fields of optimization and variational analysis.

Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces

2011-01-01 Constrained optimization
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Release : 2011-01-01
Genre : Constrained optimization
Kind : eBook
Book Rating : 692/5 ( reviews)

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Book Synopsis Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces by : Michael Ulbrich

Download or read book Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces written by Michael Ulbrich. This book was released on 2011-01-01. Available in PDF, EPUB and Kindle. Book excerpt: Semismooth Newton methods are a modern class of remarkably powerful and versatile algorithms for solving constrained optimization problems with partial differential equations (PDEs), variational inequalities, and related problems. This book provides a comprehensive presentation of these methods in function spaces, striking a balance between thoroughly developed theory and numerical applications. Although largely self-contained, the book also covers recent developments in the field, such as state-constrained problems, and offers new material on topics such as improved mesh independence results. The theory and methods are applied to a range of practically important problems, including: optimal control of nonlinear elliptic differential equations, obstacle problems, and flow control of instationary Navier-Stokes fluids. In addition, the author covers adjoint-based derivative computation and the efficient solution of Newton systems by multigrid and preconditioned iterative methods.

Stabilized Sequential Quadratic Programming for Optimization and a Stabilized Newton-type Method for Variational Problems

2007
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Release : 2007
Genre :
Kind : eBook
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Book Synopsis Stabilized Sequential Quadratic Programming for Optimization and a Stabilized Newton-type Method for Variational Problems by : Damián Fernández

Download or read book Stabilized Sequential Quadratic Programming for Optimization and a Stabilized Newton-type Method for Variational Problems written by Damián Fernández. This book was released on 2007. Available in PDF, EPUB and Kindle. Book excerpt:

Convergence and Applications of Newton-type Iterations

2008-06-12 Mathematics
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Release : 2008-06-12
Genre : Mathematics
Kind : eBook
Book Rating : 434/5 ( reviews)

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Book Synopsis Convergence and Applications of Newton-type Iterations by : Ioannis K. Argyros

Download or read book Convergence and Applications of Newton-type Iterations written by Ioannis K. Argyros. This book was released on 2008-06-12. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to a comprehensive treatment of iterative methods for solving nonlinear equations with particular emphasis on semi-local convergence analysis. Theoretical results are applied to engineering, dynamic economic systems, input-output systems, nonlinear and linear differential equations, and optimization problems. Accompanied by many exercises, some with solutions, the book may be used as a supplementary text in the classroom for an advanced course on numerical functional analysis.

Stabilized Sequential Quadratic Programming for Optimization and a Stabilized Newton-type Method for Variational Problems Without Constraint Qualifications

2007
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Release : 2007
Genre :
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Book Synopsis Stabilized Sequential Quadratic Programming for Optimization and a Stabilized Newton-type Method for Variational Problems Without Constraint Qualifications by : Damián Fernández

Download or read book Stabilized Sequential Quadratic Programming for Optimization and a Stabilized Newton-type Method for Variational Problems Without Constraint Qualifications written by Damián Fernández. This book was released on 2007. Available in PDF, EPUB and Kindle. Book excerpt:

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