Stabilized Sequential Quadratic Programming For Optimization And A Stabilized Newton Type Method For Variational Problems
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| Author | : Alexey F. Izmailov |
| Publisher | : Springer |
| Total Pages | : 587 |
| Release | : 2014-07-08 |
| Genre | : Business & Economics |
| ISBN | : 3319042475 |
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 | : |
| Publisher | : ScholarlyEditions |
| Total Pages | : 995 |
| Release | : 2012-01-09 |
| Genre | : Mathematics |
| ISBN | : 1464964793 |
Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Logic, Operations, and Computational Mathematics and Geometry. The editors have built Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Logic, Operations, and Computational Mathematics and Geometry in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
| Author | : Vinai K. Singh |
| Publisher | : Springer Nature |
| Total Pages | : 441 |
| Release | : 2021-08-23 |
| Genre | : Mathematics |
| ISBN | : 3030682811 |
This volume explores the connections between mathematical modeling, computational methods, and high performance computing, and how recent developments in these areas can help to solve complex problems in the natural sciences and engineering. The content of the book is based on talks and papers presented at the conference Modern Mathematical Methods and High Performance Computing in Science & Technology (M3HPCST), held at Inderprastha Engineering College in Ghaziabad, India in January 2020. A wide range of both theoretical and applied topics are covered in detail, including the conceptualization of infinity, efficient domain decomposition, high capacity wireless communication, infectious disease modeling, and more. These chapters are organized around the following areas: Partial and ordinary differential equations Optimization and optimal control High performance and scientific computing Stochastic models and statistics Recent Trends in Mathematical Modeling and High Performance Computing will be of interest to researchers in both mathematics and engineering, as well as to practitioners who face complex models and extensive computations.
| Author | : Jon Lee |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 687 |
| Release | : 2011-12-02 |
| Genre | : Mathematics |
| ISBN | : 1461419271 |
Many engineering, operations, and scientific applications include a mixture of discrete and continuous decision variables and nonlinear relationships involving the decision variables that have a pronounced effect on the set of feasible and optimal solutions. Mixed-integer nonlinear programming (MINLP) problems combine the numerical difficulties of handling nonlinear functions with the challenge of optimizing in the context of nonconvex functions and discrete variables. MINLP is one of the most flexible modeling paradigms available for optimization; but because its scope is so broad, in the most general cases it is hopelessly intractable. Nonetheless, an expanding body of researchers and practitioners — including chemical engineers, operations researchers, industrial engineers, mechanical engineers, economists, statisticians, computer scientists, operations managers, and mathematical programmers — are interested in solving large-scale MINLP instances.
| Author | : Christodoulos A. Floudas |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 4646 |
| Release | : 2008-09-04 |
| Genre | : Mathematics |
| ISBN | : 0387747583 |
The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".
| Author | : Kazufumi Ito |
| Publisher | : SIAM |
| Total Pages | : 354 |
| Release | : 2008-11-06 |
| Genre | : Mathematics |
| ISBN | : 0898716497 |
Analyses Lagrange multiplier theory and demonstrates its impact on the development of numerical algorithms for variational problems in function spaces.
| Author | : Aharon Ben-Tal |
| Publisher | : SIAM |
| Total Pages | : 500 |
| Release | : 2001-01-01 |
| Genre | : Technology & Engineering |
| ISBN | : 0898714915 |
Here is a book devoted to well-structured and thus efficiently solvable convex optimization problems, with emphasis on conic quadratic and semidefinite programming. The authors present the basic theory underlying these problems as well as their numerous applications in engineering, including synthesis of filters, Lyapunov stability analysis, and structural design. The authors also discuss the complexity issues and provide an overview of the basic theory of state-of-the-art polynomial time interior point methods for linear, conic quadratic, and semidefinite programming. The book's focus on well-structured convex problems in conic form allows for unified theoretical and algorithmical treatment of a wide spectrum of important optimization problems arising in applications.
| Author | : Gianni Pillo |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 297 |
| Release | : 2006-06-03 |
| Genre | : Mathematics |
| ISBN | : 0387300651 |
This book reviews and discusses recent advances in the development of methods and algorithms for nonlinear optimization and its applications, focusing on the large-dimensional case, the current forefront of much research. Individual chapters, contributed by eminent authorities, provide an up-to-date overview of the field from different and complementary standpoints, including theoretical analysis, algorithmic development, implementation issues and applications.
| Author | : Andrew Eberhard |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 309 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 1461332850 |
Although the monograph Progress in Optimization I: Contributions from Aus tralasia grew from the idea of publishing a proceedings of the Fourth Optimiza tion Day, held in July 1997 at the Royal Melbourne Institute of Technology, the focus soon changed to a refereed volume in optimization. The intention is to publish a similar book annually, following each Optimization Day. The idea of having an annual Optimization Day was conceived by Barney Glover; the first of these Optimization Days was held in 1994 at the University of Ballarat. Barney hoped that such a yearly event would bring together the many, but widely dispersed, researchers in Australia who were publishing in optimization and related areas such as control. The first Optimization Day event was followed by similar conferences at The University of New South Wales (1995), The University of Melbourne (1996), the Royal Melbourne Institute of Technology (1997), and The University of Western Australia (1998). The 1999 conference will return to Ballarat University, being organized by Barney's long-time collaborator Alex Rubinov. In recent years the Optimization Day has been held in conjunction with other locally-held national or international conferences. This has widened the scope of the monograph with contributions not only coming from researchers in Australia and neighboring regions but also from their collaborators in Europe and North America.
| Author | : Dimitri Bertsekas |
| Publisher | : Athena Scientific |
| Total Pages | : 256 |
| Release | : 2009-06-01 |
| Genre | : Mathematics |
| ISBN | : 1886529310 |
An insightful, concise, and rigorous treatment of the basic theory of convex sets and functions in finite dimensions, and the analytical/geometrical foundations of convex optimization and duality theory. Convexity theory is first developed in a simple accessible manner, using easily visualized proofs. Then the focus shifts to a transparent geometrical line of analysis to develop the fundamental duality between descriptions of convex functions in terms of points, and in terms of hyperplanes. Finally, convexity theory and abstract duality are applied to problems of constrained optimization, Fenchel and conic duality, and game theory to develop the sharpest possible duality results within a highly visual geometric framework. This on-line version of the book, includes an extensive set of theoretical problems with detailed high-quality solutions, which significantly extend the range and value of the book. The book may be used as a text for a theoretical convex optimization course; the author has taught several variants of such a course at MIT and elsewhere over the last ten years. It may also be used as a supplementary source for nonlinear programming classes, and as a theoretical foundation for classes focused on convex optimization models (rather than theory). It is an excellent supplement to several of our books: Convex Optimization Algorithms (Athena Scientific, 2015), Nonlinear Programming (Athena Scientific, 2017), Network Optimization(Athena Scientific, 1998), Introduction to Linear Optimization (Athena Scientific, 1997), and Network Flows and Monotropic Optimization (Athena Scientific, 1998).
