Augmented Lagrangian Methods For Nonsmooth Convex Optimization In Hilbert Spaces

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Lagrange Multiplier Approach to Variational Problems and Applications

Author : Kazufumi Ito
Publisher : SIAM
ISBN 13 : 9780898718614
Total Pages : 359 pages
Book Rating : 4.7/5 (186 download)

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Book Synopsis Lagrange Multiplier Approach to Variational Problems and Applications by : Kazufumi Ito

Download or read book Lagrange Multiplier Approach to Variational Problems and Applications written by Kazufumi Ito and published by SIAM. This book was released on 2008-01-01 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lagrange multiplier theory provides a tool for the analysis of a general class of nonlinear variational problems and is the basis for developing efficient and powerful iterative methods for solving these problems. This comprehensive monograph analyzes Lagrange multiplier theory and shows its impact on the development of numerical algorithms for problems posed in a function space setting. The authors develop and analyze efficient algorithms for constrained optimization and convex optimization problems based on the augumented Lagrangian concept and cover such topics as sensitivity analysis, convex optimization, second order methods, and shape sensitivity calculus. General theory is applied to challenging problems in optimal control of partial differential equations, image analysis, mechanical contact and friction problems, and American options for the Black-Scholes model.

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

Author : Michael Ulbrich
Publisher : SIAM
ISBN 13 : 9781611970692
Total Pages : 322 pages
Book Rating : 4.9/5 (76 download)

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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 and published by SIAM. This book was released on 2011-01-01 with total page 322 pages. 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.

Non-Smooth and Complementarity-Based Distributed Parameter Systems

Author : Michael Hintermüller
Publisher : Springer Nature
ISBN 13 : 3030793931
Total Pages : 518 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Non-Smooth and Complementarity-Based Distributed Parameter Systems by : Michael Hintermüller

Download or read book Non-Smooth and Complementarity-Based Distributed Parameter Systems written by Michael Hintermüller and published by Springer Nature. This book was released on 2022-02-18 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many of the most challenging problems in the applied sciences involve non-differentiable structures as well as partial differential operators, thus leading to non-smooth distributed parameter systems. This edited volume aims to establish a theoretical and numerical foundation and develop new algorithmic paradigms for the treatment of non-smooth phenomena and associated parameter influences. Other goals include the realization and further advancement of these concepts in the context of robust and hierarchical optimization, partial differential games, and nonlinear partial differential complementarity problems, as well as their validation in the context of complex applications. Areas for which applications are considered include optimal control of multiphase fluids and of superconductors, image processing, thermoforming, and the formation of rivers and networks. Chapters are written by leading researchers and present results obtained in the first funding phase of the DFG Special Priority Program on Nonsmooth and Complementarity Based Distributed Parameter Systems: Simulation and Hierarchical Optimization that ran from 2016 to 2019.

From Convexity to Nonconvexity

Author : R.P. Gilbert
Publisher : Springer Science & Business Media
ISBN 13 : 1461302870
Total Pages : 395 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis From Convexity to Nonconvexity by : R.P. Gilbert

Download or read book From Convexity to Nonconvexity written by R.P. Gilbert and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of papers is dedicated to the memory of Gaetano Fichera, a great mathematician and also a good friend to the editors. Regrettably it took an unusual amount of time to bring this collection out. This was primarily due to the fact that the main editor who had collected all of the materials, for this volume, P. D. Panagiotopoulos, died unexpectedly during the period when we were editing the manuscript. The other two editors in appreciation of Panagiotopoulos' contribution to this field, believe it is therefore fitting that this collection be dedicated to his memory also. The theme of the collection is centered around the seminal research of G. Fichera on the Signorini problem. Variants on this idea enter in different ways. For example, by bringing in friction the problem is no longer self-adjoint and the minimization formulation is not valid. A large portion of this collection is devoted to survey papers concerning hemivariational methods, with a main point of its application to nonsmooth mechanics. Hemivariational inequali ties, which are a generalization of variational inequalities, were pioneered by Panagiotopoulos. There are many applications of this theory to the study of non convex energy functionals occurring in many branches of mechanics. An area of concentration concerns contact problems, in particular, quasistatic and dynamic contact problems with friction and damage. Nonsmooth optimization methods which may be divided into the main groups of subgradient methods and bundle methods are also discussed in this collection.

Control of Partial Differential Equations and Applications

Author : Eduardo Casas
Publisher : CRC Press
ISBN 13 : 9780824796075
Total Pages : 324 pages
Book Rating : 4.7/5 (96 download)

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Book Synopsis Control of Partial Differential Equations and Applications by : Eduardo Casas

Download or read book Control of Partial Differential Equations and Applications written by Eduardo Casas and published by CRC Press. This book was released on 1995-09-20 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the International Federation for Information Processing TC7/WG-7.2 Conference, held in Laredo, Spain, this work covers theoretical advances as well as results on control problems and applications for partial differential equations. It examines the controllability and stabilization of distributed sytems, optimality conditions, shape optimization and numerical methods.

Optimal Control of Partial Differential Equations

Author : Fredi Tröltzsch
Publisher : American Mathematical Soc.
ISBN 13 : 0821849042
Total Pages : 418 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Optimal Control of Partial Differential Equations by : Fredi Tröltzsch

Download or read book Optimal Control of Partial Differential Equations written by Fredi Tröltzsch and published by American Mathematical Soc.. This book was released on 2010 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal control theory is concerned with finding control functions that minimize cost functions for systems described by differential equations. This book focuses on optimal control problems where the state equation is an elliptic or parabolic partial differential equation. It includes topics on the existence of optimal solutions.

Recent Developments in Optimization Theory and Nonlinear Analysis

Author : Yair Censor
Publisher : American Mathematical Soc.
ISBN 13 : 0821805150
Total Pages : 290 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Recent Developments in Optimization Theory and Nonlinear Analysis by : Yair Censor

Download or read book Recent Developments in Optimization Theory and Nonlinear Analysis written by Yair Censor and published by American Mathematical Soc.. This book was released on 1997 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the refereed proceedings of the special session on Optimization and Nonlinear Analysis held at the Joint American Mathematical Society-Israel Mathematical Union Meeting which took place at the Hebrew University of Jerusalem in May 1995. Most of the papers in this book originated from the lectures delivered at this special session. In addition, some participants who didn't present lectures and invited speakers who were unable to attend contributed their work. The fields of optimization theory and nonlinear analysis continue to be very active. This book presents not only the wide spectrum and diversity of the results, but also their manifold connections to other areas, such as differential equations, functional analysis, operator theory, calculus of variations, numerical analysis, and mathematical programming. In reading this book one encounters papers that deal, for example, with convex, quasiconvex and generalized convex functions, fixed and periodic points, fractional-linear transformations, moduli of convexity, monontone operators, Morse lemmas, Navier-Stokes equations, nonexpansive maps, nonsmooth analysis, numerical stability, products of projections, steepest descent, the Leray-Schauder degree, the turnpike property, and variational inequalities.

Control of Coupled Partial Differential Equations

Author : Karl Kunisch
Publisher : Springer Science & Business Media
ISBN 13 : 3764377216
Total Pages : 384 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Control of Coupled Partial Differential Equations by : Karl Kunisch

Download or read book Control of Coupled Partial Differential Equations written by Karl Kunisch and published by Springer Science & Business Media. This book was released on 2007-08-08 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains selected contributions originating from the ‘Conference on Optimal Control of Coupled Systems of Partial Differential Equations’, held at the ‘Mathematisches Forschungsinstitut Oberwolfach’ in April 2005. With their articles, leading scientists cover a broad range of topics such as controllability, feedback-control, optimality systems, model-reduction techniques, analysis and optimal control of flow problems, and fluid-structure interactions, as well as problems of shape and topology optimization. Applications affected by these findings are distributed over all time and length scales starting with optimization and control of quantum mechanical systems, the design of piezoelectric acoustic micro-mechanical devices, or optimal control of crystal growth to the control of bodies immersed into a fluid, airfoil design, and much more. The book addresses advanced students and researchers in optimization and control of infinite dimensional systems, typically represented by partial differential equations. Readers interested either in theory or in numerical simulation of such systems will find this book equally appealing.

IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22–25, 2018

Author : Jörg Fehr
Publisher : Springer
ISBN 13 : 3030210138
Total Pages : 229 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22–25, 2018 by : Jörg Fehr

Download or read book IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22–25, 2018 written by Jörg Fehr and published by Springer. This book was released on 2019-07-19 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the IUTAM Symposium on Model Order Reduction of Coupled System, held in Stuttgart, Germany, May 22–25, 2018. For the understanding and development of complex technical systems, such as the human body or mechatronic systems, an integrated, multiphysics and multidisciplinary view is essential. Many problems can be solved within one physical domain. For the simulation and optimization of the combined system, the different domains are connected with each other. Very often, the combination is only possible by using reduced order models such that the large-scale dynamical system is approximated with a system of much smaller dimension where the most dominant features of the large-scale system are retained as much as possible. The field of model order reduction (MOR) is interdisciplinary. Researchers from Engineering, Mathematics and Computer Science identify, explore and compare the potentials, challenges and limitations of recent and new advances.

Contact Mechanics

Author : J.A.C. Martins
Publisher : Springer Science & Business Media
ISBN 13 : 9401711542
Total Pages : 442 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Contact Mechanics by : J.A.C. Martins

Download or read book Contact Mechanics written by J.A.C. Martins and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 44 papers presented at the Third Contact Mechanics International Symposium (CMIS 2001) held in Praia da Consola9ao, Peniche (portugal), June 17-21,2001. This Symposium was the direct continuation of the first two CMIS held in Lausanne (1992) and in Carry-Le-Rouet (1994). Other related meetings, in what concerns scientific topics and participants, took place in the nineties at La Grande Motte (1990), Vadstena (1996), Ferrara (1997), Munich (1998) and Grenoble (1999). The Symposium aimed at gathering researchers with interests in a wide range of topics in theoretical, computational and experimental contact mechanics. The call for papers mentioned topics in tribology, mathematical formulations and analysis, numerical methods in non-smooth mechanics, impact problems, instabilities and technological problems. The total number of participants was 102, from Universities and Research Institutes of 19 countries. The Scientific Committee reviewed 102 submitted abstracts, and the final program consisted of 6 main lectures, 43 oral communications and 36 poster presentations (see Appendix A). The papers in this book correspond to almost all the main lectures and oral communications, and they are assembled in 5 chapters: • Dynamics and Impact • Instabilities, Oscillations and Waves • Contact Models, Results and Applications • Mathematical Analysis • Numerical Methods. We thank all the authors for their valuable contributions to this volume. We are indebted to the members of the Scientific Committee for their help in refereeing the submitted abstracts and manuscripts. We also thank the Series editor, Prof. Graham Gladwell, for his assistance in the revision process.

Fast Solution of Discretized Optimization Problems

Author : Karl-Heinz Hoffmann
Publisher : Birkhäuser
ISBN 13 : 3034882335
Total Pages : 292 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Fast Solution of Discretized Optimization Problems by : Karl-Heinz Hoffmann

Download or read book Fast Solution of Discretized Optimization Problems written by Karl-Heinz Hoffmann and published by Birkhäuser. This book was released on 2012-12-06 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Control and Estimation of Distributed Parameter Systems

Author : W. Desch
Publisher : Birkhäuser
ISBN 13 : 303488849X
Total Pages : 308 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Control and Estimation of Distributed Parameter Systems by : W. Desch

Download or read book Control and Estimation of Distributed Parameter Systems written by W. Desch and published by Birkhäuser. This book was released on 2012-12-06 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Consisting of 23 refereed contributions, this volume offers a broad and diverse view of current research in control and estimation of partial differential equations. Topics addressed include, but are not limited to - control and stability of hyperbolic systems related to elasticity, linear and nonlinear; - control and identification of nonlinear parabolic systems; - exact and approximate controllability, and observability; - Pontryagin's maximum principle and dynamic programming in PDE; and - numerics pertinent to optimal and suboptimal control problems. This volume is primarily geared toward control theorists seeking information on the latest developments in their area of expertise. It may also serve as a stimulating reader to any researcher who wants to gain an impression of activities at the forefront of a vigorously expanding area in applied mathematics.

Numerical Mathematics and Advanced Applications

Author : Alfredo Bermúdez de Castro
Publisher : Springer Science & Business Media
ISBN 13 : 3540342885
Total Pages : 1202 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Numerical Mathematics and Advanced Applications by : Alfredo Bermúdez de Castro

Download or read book Numerical Mathematics and Advanced Applications written by Alfredo Bermúdez de Castro and published by Springer Science & Business Media. This book was released on 2007-10-08 with total page 1202 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings collect lectures given at ENUMATH 2005, the 6th European Conference on Numerical Mathematics and Advanced Applications held in Santiago de Compostela, Spain in July, 2005. Topics include applications such as fluid dynamics, electromagnetism, structural mechanics, interface problems, waves, finance, heat transfer, unbounded domains, numerical linear algebra, convection-diffusion, as well as methodologies such as a posteriori error estimates, discontinuous Galerkin methods, multiscale methods, optimization, and more.

SIAM Journal on Control and Optimization

Author : Society for Industrial and Applied Mathematics
Publisher :
ISBN 13 :
Total Pages : 800 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis SIAM Journal on Control and Optimization by : Society for Industrial and Applied Mathematics

Download or read book SIAM Journal on Control and Optimization written by Society for Industrial and Applied Mathematics and published by . This book was released on 2005 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Numerical Methods for Mixed Finite Element Problems

Author : Jean Deteix
Publisher : Springer Nature
ISBN 13 : 3031126165
Total Pages : 119 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Numerical Methods for Mixed Finite Element Problems by : Jean Deteix

Download or read book Numerical Methods for Mixed Finite Element Problems written by Jean Deteix and published by Springer Nature. This book was released on 2022-09-24 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on iterative solvers and preconditioners for mixed finite element methods. It provides an overview of some of the state-of-the-art solvers for discrete systems with constraints such as those which arise from mixed formulations. Starting by recalling the basic theory of mixed finite element methods, the book goes on to discuss the augmented Lagrangian method and gives a summary of the standard iterative methods, describing their usage for mixed methods. Here, preconditioners are built from an approximate factorisation of the mixed system. A first set of applications is considered for incompressible elasticity problems and flow problems, including non-linear models. An account of the mixed formulation for Dirichlet’s boundary conditions is then given before turning to contact problems, where contact between incompressible bodies leads to problems with two constraints. This book is aimed at graduate students and researchers in the field of numerical methods and scientific computing.

Scale Space and Variational Methods in Computer Vision

Author : Xue-Cheng Tai
Publisher : Springer Science & Business Media
ISBN 13 : 3642022553
Total Pages : 882 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Scale Space and Variational Methods in Computer Vision by : Xue-Cheng Tai

Download or read book Scale Space and Variational Methods in Computer Vision written by Xue-Cheng Tai and published by Springer Science & Business Media. This book was released on 2009-05-25 with total page 882 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Second International Conference on Scale Space Methods and Variational Methods in Computer Vision, SSVM 2009, emanated from the joint edition of the 5th International Workshop on Variational, Geometric and Level Set Methods in Computer Vision, VLSM 2009 and the 7th International Conference on Scale Space and PDE Methods in Computer Vision, Scale-Space 2009, held in Voss, Norway in June 2009. The 71 revised full papers presented were carefully reviewed and selected numerous submissions. The papers are organized in topical sections on segmentation and detection; image enhancement and reconstruction; motion analysis, optical flow, registration and tracking; surfaces and shapes; scale space and feature extraction.

Quantum Control: Mathematical and Numerical Challenges

Author : André D. Bandrauk
Publisher : American Mathematical Soc.
ISBN 13 : 9780821833308
Total Pages : 228 pages
Book Rating : 4.8/5 (333 download)

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Book Synopsis Quantum Control: Mathematical and Numerical Challenges by : André D. Bandrauk

Download or read book Quantum Control: Mathematical and Numerical Challenges written by André D. Bandrauk and published by American Mathematical Soc.. This book was released on 2003 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: It brought together mathematicians, theoretical chemists, and physicists working in the area of control and optimization of systems to address the outstanding numerical and mathematical problems."