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Author: Alexey F. Izmailov Publisher: Springer ISBN: 3319042475 Category : Business & Economics Languages : en Pages : 587
Book Description
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.
Author: Alexey F. Izmailov Publisher: Springer ISBN: 3319042475 Category : Business & Economics Languages : en Pages : 587
Book Description
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.
Author: Michael Ulbrich Publisher: SIAM ISBN: 9781611970692 Category : Constrained optimization Languages : en Pages : 322
Book Description
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.
Author: Ioannis K. Argyros Publisher: Springer Science & Business Media ISBN: 0387727434 Category : Mathematics Languages : en Pages : 513
Book Description
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.
Author: Kazufumi Ito Publisher: SIAM ISBN: 0898716497 Category : Mathematics Languages : en Pages : 354
Book Description
Analyses Lagrange multiplier theory and demonstrates its impact on the development of numerical algorithms for variational problems in function spaces.
Author: Alexander J. Zaslavski Publisher: Springer ISBN: 3319309218 Category : Mathematics Languages : en Pages : 308
Book Description
This book studies the approximate solutions of optimization problems in the presence of computational errors. A number of results are presented on the convergence behavior of algorithms in a Hilbert space; these algorithms are examined taking into account computational errors. The author illustrates that algorithms generate a good approximate solution, if computational errors are bounded from above by a small positive constant. Known computational errors are examined with the aim of determining an approximate solution. Researchers and students interested in the optimization theory and its applications will find this book instructive and informative. This monograph contains 16 chapters; including a chapters devoted to the subgradient projection algorithm, the mirror descent algorithm, gradient projection algorithm, the Weiszfelds method, constrained convex minimization problems, the convergence of a proximal point method in a Hilbert space, the continuous subgradient method, penalty methods and Newton’s method.
Author: Asen L. Dontchev Publisher: Springer Nature ISBN: 3030799115 Category : Mathematics Languages : en Pages : 223
Book Description
This book presents an introduction to variational analysis, a field which unifies theories and techniques developed in calculus of variations, optimization, and control, and covers convex analysis, nonsmooth analysis, and set-valued analysis. It focuses on problems with constraints, the analysis of which involves set-valued mappings and functions that are not differentiable. Applications of variational analysis are interdisciplinary, ranging from financial planning to steering a flying object. The book is addressed to graduate students, researchers, and practitioners in mathematical sciences, engineering, economics, and finance. A typical reader of the book should be familiar with multivariable calculus and linear algebra. Some basic knowledge in optimization, control, and elementary functional analysis is desirable, but all necessary background material is included in the book.
Author: Michael C. Ferris Publisher: SIAM ISBN: 9780898713916 Category : Mathematics Languages : en Pages : 494
Book Description
After more than three decades of research, the subject of complementarity problems and its numerous extensions has become a well-established and fruitful discipline within mathematical programming and applied mathematics. Sources of these problems are diverse and span numerous areas in engineering, economics, and the sciences. Includes refereed articles.
Author: Alexey F. Izmailov
Author: Alexey F. Izmailov
Author: Michael Ulbrich
Author: Damián Fernández
Author: Ioannis K. Argyros
Author: Kazufumi Ito
Author: Damián Fernández
Author: Alexander J. Zaslavski
Author: Boris S. Mordukhovich
Author: Asen L. Dontchev
Author: Michael C. Ferris