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First Order Augmented Lagrangian Methods For State Constraint Problems
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Book Synopsis Practical Augmented Lagrangian Methods for Constrained Optimization by : Ernesto G. Birgin
Download or read book Practical Augmented Lagrangian Methods for Constrained Optimization written by Ernesto G. Birgin and published by SIAM. This book was released on 2014-04-30 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on Augmented Lagrangian techniques for solving practical constrained optimization problems. The authors rigorously delineate mathematical convergence theory based on sequential optimality conditions and novel constraint qualifications. They also orient the book to practitioners by giving priority to results that provide insight on the practical behavior of algorithms and by providing geometrical and algorithmic interpretations of every mathematical result, and they fully describe a freely available computational package for constrained optimization and illustrate its usefulness with applications.
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 2008-11-06 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analyses Lagrange multiplier theory and demonstrates its impact on the development of numerical algorithms for variational problems in function spaces.
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.
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.
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.
Book Synopsis Constrained Optimization and Lagrange Multiplier Methods by : Dimitri P. Bertsekas
Download or read book Constrained Optimization and Lagrange Multiplier Methods written by Dimitri P. Bertsekas and published by Academic Press. This book was released on 2014-05-10 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer Science and Applied Mathematics: Constrained Optimization and Lagrange Multiplier Methods focuses on the advancements in the applications of the Lagrange multiplier methods for constrained minimization. The publication first offers information on the method of multipliers for equality constrained problems and the method of multipliers for inequality constrained and nondifferentiable optimization problems. Discussions focus on approximation procedures for nondifferentiable and ill-conditioned optimization problems; asymptotically exact minimization in the methods of multipliers; duality framework for the method of multipliers; and the quadratic penalty function method. The text then examines exact penalty methods, including nondifferentiable exact penalty functions; linearization algorithms based on nondifferentiable exact penalty functions; differentiable exact penalty functions; and local and global convergence of Lagrangian methods. The book ponders on the nonquadratic penalty functions of convex programming. Topics include large scale separable integer programming problems and the exponential method of multipliers; classes of penalty functions and corresponding methods of multipliers; and convergence analysis of multiplier methods. The text is a valuable reference for mathematicians and researchers interested in the Lagrange multiplier methods.
Author :Karl-Heinz Hoffmann Publisher :Springer Science & Business Media ISBN 13 :9783764365998 Total Pages :308 pages Book Rating :4.3/5 (659 download)
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 Springer Science & Business Media. This book was released on 2001-09-01 with total page 308 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.
Book Synopsis Constrained Markov Decision Processes by : Eitan Altman
Download or read book Constrained Markov Decision Processes written by Eitan Altman and published by Routledge. This book was released on 2021-12-17 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unified approach for the study of constrained Markov decision processes with a finite state space and unbounded costs. Unlike the single controller case considered in many other books, the author considers a single controller with several objectives, such as minimizing delays and loss, probabilities, and maximization of throughputs. It is desirable to design a controller that minimizes one cost objective, subject to inequality constraints on other cost objectives. This framework describes dynamic decision problems arising frequently in many engineering fields. A thorough overview of these applications is presented in the introduction. The book is then divided into three sections that build upon each other.
Book Synopsis Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers by : Stephen Boyd
Download or read book Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers written by Stephen Boyd and published by Now Publishers Inc. This book was released on 2011 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: Surveys the theory and history of the alternating direction method of multipliers, and discusses its applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others.
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.
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.
Book Synopsis Optimization Methods in Partial Differential Equations by : Steven Cox
Download or read book Optimization Methods in Partial Differential Equations written by Steven Cox and published by American Mathematical Soc.. This book was released on 1997 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problems considered range from basic theoretical issues in the calculus of variations - such as infinite dimensional Hamilton Jacobi equations, saddle point principles, and issues of unique continuation - to ones focusing on application and computation, where theoretical tools are tuned to more specifically defined problems.
Book Synopsis Mathematical Programming The State of the Art by : A. Bachem
Download or read book Mathematical Programming The State of the Art written by A. Bachem and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the late forties, Mathematical Programming became a scientific discipline in its own right. Since then it has experienced a tremendous growth. Beginning with economic and military applications, it is now among the most important fields of applied mathematics with extensive use in engineering, natural sciences, economics, and biological sciences. The lively activity in this area is demonstrated by the fact that as early as 1949 the first "Symposium on Mathe matical Programming" took place in Chicago. Since then mathematical programmers from all over the world have gath ered at the intfrnational symposia of the Mathematical Programming Society roughly every three years to present their recent research, to exchange ideas with their colleagues and to learn about the latest developments in their own and related fields. In 1982, the XI. International Symposium on Mathematical Programming was held at the University of Bonn, W. Germany, from August 23 to 27. It was organized by the Institut fUr Okonometrie und Operations Re search of the University of Bonn in collaboration with the Sonderforschungs bereich 21 of the Deutsche Forschungsgemeinschaft. This volume constitutes part of the outgrowth of this symposium and docu ments its scientific activities. Part I of the book contains information about the symposium, welcoming addresses, lists of committees and sponsors and a brief review about the Ful kerson Prize and the Dantzig Prize which were awarded during the opening ceremony.
Book Synopsis Nuclear Density Functional Theory by : I. Zh Petkov
Download or read book Nuclear Density Functional Theory written by I. Zh Petkov and published by . This book was released on 1991 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book summarizes the enormous amount of material accumulated in the field of nuclear density functional theory over the last few decades. The goal of the theory is to provide a complete quantum mechanical description and explanation of nuclear phenomena in terms of the local density distribution as a basic ingredient rather than the many particle wavefunction. This leads to a considerable reduction in the mathematical complexity of nuclear many-body problems and to a great conceptual simplicity and visual clarity in its theoretical treatment. The authors develop the mathematical framework on which the theory is based and consider the associated approaches used to analyze experimental data in a variety of nuclei and nuclear processes with widely differing properties.
Book Synopsis Mesh Dependence in PDE-Constrained Optimisation by : Tobias Schwedes
Download or read book Mesh Dependence in PDE-Constrained Optimisation written by Tobias Schwedes and published by Springer. This book was released on 2017-07-07 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to PDE-constrained optimisation using finite elements and the adjoint approach. The practical impact of the mathematical insights presented here are demonstrated using the realistic scenario of the optimal placement of marine power turbines, thereby illustrating the real-world relevance of best-practice Hilbert space aware approaches to PDE-constrained optimisation problems. Many optimisation problems that arise in a real-world context are constrained by partial differential equations (PDEs). That is, the system whose configuration is to be optimised follows physical laws given by PDEs. This book describes general Hilbert space formulations of optimisation algorithms, thereby facilitating optimisations whose controls are functions of space. It demonstrates the importance of methods that respect the Hilbert space structure of the problem by analysing the mathematical drawbacks of failing to do so. The approaches considered are illustrated using the optimisation problem arising in tidal array layouts mentioned above. This book will be useful to readers from engineering, computer science, mathematics and physics backgrounds interested in PDE-constrained optimisation and their real-world applications.
Book Synopsis Developments in Model-Based Optimization and Control by : Sorin Olaru
Download or read book Developments in Model-Based Optimization and Control written by Sorin Olaru and published by Springer. This book was released on 2015-12-23 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with optimization methods as tools for decision making and control in the presence of model uncertainty. It is oriented to the use of these tools in engineering, specifically in automatic control design with all its components: analysis of dynamical systems, identification problems, and feedback control design. Developments in Model-Based Optimization and Control takes advantage of optimization-based formulations for such classical feedback design objectives as stability, performance and feasibility, afforded by the established body of results and methodologies constituting optimal control theory. It makes particular use of the popular formulation known as predictive control or receding-horizon optimization. The individual contributions in this volume are wide-ranging in subject matter but coordinated within a five-part structure covering material on: · complexity and structure in model predictive control (MPC); · collaborative MPC; · distributed MPC; · optimization-based analysis and design; and · applications to bioprocesses, multivehicle systems or energy management. The various contributions cover a subject spectrum including inverse optimality and more modern decentralized and cooperative formulations of receding-horizon optimal control. Readers will find fourteen chapters dedicated to optimization-based tools for robustness analysis, and decision-making in relation to feedback mechanisms—fault detection, for example—and three chapters putting forward applications where the model-based optimization brings a novel perspective. Developments in Model-Based Optimization and Control is a selection of contributions expanded and updated from the Optimisation-based Control and Estimation workshops held in November 2013 and November 2014. It forms a useful resource for academic researchers and graduate students interested in the state of the art in predictive control. Control engineers working in model-based optimization and control, particularly in its bioprocess applications will also find this collection instructive.
Book Synopsis Inverse Problems in Diffusion Processes by : Heinz W. Engl
Download or read book Inverse Problems in Diffusion Processes written by Heinz W. Engl and published by SIAM. This book was released on 1995-01-01 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of expository papers encompasses both the theoretical and physical application side of inverse problems in diffusion processes.
