Fast Solution Of Discretized Optimization Problems
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Fast Solution Of Discretized Optimization Problems
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Author : Karl-Heinz Hoffmann
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Fast Solution Of Discretized Optimization Problems written by Karl-Heinz Hoffmann and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A collection of articles summarizing the state of knowledge in a large portion of modern homotopy theory. This welcome reference for many new results and recent methods is addressed to all mathematicians interested in homotopy theory and in geometric aspects of group theory.
Fast Solution Of Discretized Optimization Problems
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Author : Karl-Heinz Hoffmann
language : en
Publisher: Birkhauser
Release Date : 2001-01-01
Fast Solution Of Discretized Optimization Problems written by Karl-Heinz Hoffmann and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Mathematics categories.
This book contains a collection of articles summarizing the state of knowledge in a large portion of modern homotopy theory. A call for articles was made on the occasion of an emphasis semester organized by the Centre de Recerca MatemA tica in Bellaterra (Barcelona) in 1998. The main topics treated in the book include abstract features of stable and unstable homotopy, homotopical localizations, p-compact groups, H-spaces, classifying spaces for proper actions, cohomology of discrete groups, K-theory and other generalized cohomology theories, configuration spaces, and Lusternik-Schnirelmann category.The book is addressed to all mathematicians interested in homotopy theory and in geometric aspects of group theory. New research directions in topology are highlighted. Moreover, this informative and educational book serves as a welcome reference for many new results and recent methods
Discretization Methods And Structural Optimization Procedures And Applications
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Author : Hans A. Eschenauer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Discretization Methods And Structural Optimization Procedures And Applications written by Hans A. Eschenauer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
In recent years, the Finite Element Methods FEM were more and more employed in development and design departments as very fast working tools in order to determine stresses, deformations, eigenfrequencies etc. for all kinds of constructions under complex loading conditions. Meanwhile. very effective software systems have been developed by various research teams although some mathematical problems (e. g. convergence) have not been solved satisfac torily yet. In order to make further advances and to find a common language between mathe maticians and mechanicians the "Society for Applied Mathematics and Mechanics" (GAMM) agreed on the foundation of a special Committee: "Discretization Methods in Solid Mechanics" focussing on the following problems: - Structuring of various methods (displacement functions, hybrid and mixed approaches, etc. >, - Survey of approach functions (Lagrange-/Hermite-polynominals, Spline-functions), - Description of singularities, - Convergence and stability, - Practical and theoretical optimality to all mentioned issues (single and interacting). One of the basic aims of the GAMM-Committee is the interdisciplinary cooperation between mechanicians, mathematicians, and users which shall be intensified. Thus, on September 22, 1985 the committee decided to hold a seminar on "Structural Optimization" in order to allow an exchange of experiences and thoughts between the experts of finite element methods and those of structural optimization. A GAMM-seminar entitled "Discretization Methods and Structural Optimization - Procedures and Applications" was hold on October 5-7, 1988 at the Unversity of Siegen.
Discrete Optimization
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Author : E. Boros
language : en
Publisher: Elsevier
Release Date : 2003-03-19
Discrete Optimization written by E. Boros and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-19 with Mathematics categories.
One of the most frequently occurring types of optimization problems involves decision variables which have to take integer values. From a practical point of view, such problems occur in countless areas of management, engineering, administration, etc., and include such problems as location of plants or warehouses, scheduling of aircraft, cutting raw materials to prescribed dimensions, design of computer chips, increasing reliability or capacity of networks, etc. This is the class of problems known in the professional literature as "discrete optimization" problems. While these problems are of enormous applicability, they present many challenges from a computational point of view. This volume is an update on the impressive progress achieved by mathematicians, operations researchers, and computer scientists in solving discrete optimization problems of very large sizes. The surveys in this volume present a comprehensive overview of the state of the art in discrete optimization and are written by the most prominent researchers from all over the world. This volume describes the tremendous progress in discrete optimization achieved in the last 20 years since the publication of Discrete Optimization '77, Annals of Discrete Mathematics, volumes 4 and 5, 1979 (Elsevier). It contains surveys of the state of the art written by the most prominent researchers in the field from all over the world, and covers topics like neighborhood search techniques, lift and project for mixed 0-1 programming, pseudo-Boolean optimization, scheduling and assignment problems, production planning, location, bin packing, cutting planes, vehicle routing, and applications to graph theory, mechanics, chip design, etc. Key features: • state of the art surveys • comprehensiveness • prominent authors • theoretical, computational and applied aspects. This book is a reprint of Discrete Applied Mathematics Volume 23, Numbers 1-3
Approximation And Complexity In Numerical Optimization
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Author : Panos M. Pardalos
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-05-31
Approximation And Complexity In Numerical Optimization written by Panos M. Pardalos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-05-31 with Technology & Engineering categories.
There has been much recent progress in approximation algorithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective. In discrete (or combinatorial) optimization many approaches have been developed recently that link the discrete universe to the continuous universe through geomet ric, analytic, and algebraic techniques. Such techniques include global optimization formulations, semidefinite programming, and spectral theory. As a result new ap proximate algorithms have been discovered and many new computational approaches have been developed. Similarly, for many continuous nonconvex optimization prob lems, new approximate algorithms have been developed based on semidefinite pro gramming and new randomization techniques. On the other hand, computational complexity, originating from the interactions between computer science and numeri cal optimization, is one of the major theories that have revolutionized the approach to solving optimization problems and to analyzing their intrinsic difficulty. The main focus of complexity is the study of whether existing algorithms are efficient for the solution of problems, and which problems are likely to be tractable. The quest for developing efficient algorithms leads also to elegant general approaches for solving optimization problems, and reveals surprising connections among problems and their solutions. A conference on Approximation and Complexity in Numerical Optimization: Con tinuous and Discrete Problems was held during February 28 to March 2, 1999 at the Center for Applied Optimization of the University of Florida.
Discrete Optimization I
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Author :
language : en
Publisher: Elsevier
Release Date : 2000-04-01
Discrete Optimization I written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-01 with Mathematics categories.
Discrete Optimization I
Novel Approaches To Hard Discrete Optimization
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Author : Panos M. Pardalos
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Novel Approaches To Hard Discrete Optimization written by Panos M. Pardalos and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
During the last decade, many novel approaches have been considered for dealing with computationally difficult discrete optimization problems. Such approaches include interior point methods, semidefinite programming techniques, and global optimization. More efficient computational algorithms have been developed and larger problem instances of hard discrete problems have been solved. This progress is due in part to these novel approaches, but also to new computing facilities and massive parallelism. This volume contains the papers presented at the workshop on ``Novel Approaches to Hard Discrete Optimization''. The articles cover a spectrum of issues regarding computationally hard discrete problems.
Fast Tensor Product Solvers For Optimization Problems With Fractional Differential Equations As Constraints
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Author : Sergey Dolgov
language : en
Publisher:
Release Date : 2015
Fast Tensor Product Solvers For Optimization Problems With Fractional Differential Equations As Constraints written by Sergey Dolgov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
Abstract: Fractional differential equations have recently received much attention within computational mathematics and applied science, and their numerical treatment is an important research area as such equations pose substantial challenges to existing algorithms. An optimization problem with constraints given by fractional differential equations is considered, which in its discretized form leads to a high-dimensional tensor equation. The solution to such equations is presented in the tensor-train format. We compare three types of solution strategies that employ sophisticated iterative techniques using either preconditioned Krylov solvers or tailored alternating schemes. The competitiveness of these approaches is presented using several examples.
A Direct Method For Parabolic Pde Constrained Optimization Problems
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Author : Andreas Potschka
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-29
A Direct Method For Parabolic Pde Constrained Optimization Problems written by Andreas Potschka and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-29 with Mathematics categories.
Andreas Potschka discusses a direct multiple shooting method for dynamic optimization problems constrained by nonlinear, possibly time-periodic, parabolic partial differential equations. In contrast to indirect methods, this approach automatically computes adjoint derivatives without requiring the user to formulate adjoint equations, which can be time-consuming and error-prone. The author describes and analyzes in detail a globalized inexact Sequential Quadratic Programming method that exploits the mathematical structures of this approach and problem class for fast numerical performance. The book features applications, including results for a real-world chemical engineering separation problem.
Scalable Algorithms For Contact Problems
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Author : Zdeněk Dostál
language : en
Publisher: Springer Nature
Release Date : 2023-11-29
Scalable Algorithms For Contact Problems written by Zdeněk Dostál and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-29 with Mathematics categories.
This book presents a comprehensive treatment of recently developed scalable algorithms for solving multibody contact problems of linear elasticity. The brand-new feature of these algorithms is their theoretically supported numerical scalability (i.e., asymptotically linear complexity) and parallel scalability demonstrated in solving problems discretized by billions of degrees of freedom. The theory covers solving multibody frictionless contact problems, contact problems with possibly orthotropic Tresca’s friction, and transient contact problems. In addition, it also covers BEM discretization, treating jumping coefficients, floating bodies, mortar non-penetration conditions, etc. This second edition includes updated content, including a new chapter on hybrid domain decomposition methods for huge contact problems. Furthermore, new sections describe the latest algorithm improvements, e.g., the fast reconstruction of displacements, the adaptive reorthogonalization of dual constraints, and an updated chapter on parallel implementation. Several chapters are extended to give an independent exposition of classical bounds on the spectrum of mass and dual stiffness matrices, a benchmark for Coulomb orthotropic friction, details of discretization, etc. The exposition is divided into four parts, the first of which reviews auxiliary linear algebra, optimization, and analysis. The most important algorithms and optimality results are presented in the third chapter. The presentation includes continuous formulation, discretization, domain decomposition, optimality results, and numerical experiments. The final part contains extensions to contact shape optimization, plasticity, and HPC implementation. Graduate students and researchers in mechanical engineering, computational engineering, and applied mathematics will find this book of great value and interest.