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Book
Semismooth Newton methods for variational inequalities and constrained optimization problems in function spaces
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ISBN: 1611970687 9781611970685 Year: 2011 Publisher: Philadelphia: Society for industrial and applied mathematics,

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Book
Nichtlineare Optimierung
Authors: ---
ISBN: 3034606540 Year: 2012 Publisher: Basel : Springer Basel : Imprint: Birkhäuser,

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Das Buch gibt eine Einführung in zentrale Konzepte und Methoden der Nichtlinearen Optimierung. Es ist aus Vorlesungen der Autoren an der TU München, der TU Darmstadt und der Universität Hamburg entstanden. Der Inhalt des Buches wurde insbesondere auf mathematische Bachelorstudiengänge zugeschnitten und hat sich als Basis entsprechender Vorlesungen sowie für eine anschließende Vertiefung im Bereich der Optimierung bewährt. Der Umfang entspricht zwei zweistündigen oder einer vierstündigen Vorlesung, wobei etwa in gleichem Umfang sowohl unrestringierte Optimierungsprobleme als auch Optimierungsprobleme mit Nebenbedingungen behandelt werden. Im Teil über die unrestringierte Optimierung werden sowohl Trust-Region- als auch Liniensuch-Methoden zur Globalisierung behandelt. Für letztere wird ein ebenso leistungsfähiges wie intuitives Konzept der zulässigen Suchrichtungen und Schrittweiten entwickelt. Die schnelle lokale Konvergenz Newton-artiger Verfahren und ihre Globalisierung sind weitere wichtige Themengebiete. Das Kapitel über restringierte Optimierung entwickelt notwendige und hinreichende Optimalitätsbedingungen und geht auf wichtige numerische Verfahren, insbesondere Sequential Quadratic Programming, Penalty- und Barriereverfahren ein. Der Bezug von Barriereverfahren zu den aktuell intensiv untersuchten Innere-Punkte-Verfahren wird ebenfalls hergestellt.


Book
Optimization with PDE constraints
Authors: --- ---
ISBN: 9789048180035 Year: 2009 Publisher: Dordrecht Springer

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Digital
Optimization with PDE constraints
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ISBN: 9781402088391 9781402088384 Year: 2009 Publisher: Dordrecht Springer Netherlands

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Book
Non-Smooth and Complementarity-Based Distributed Parameter Systems
Authors: --- --- --- --- --- et al.
ISBN: 9783030793937 Year: 2022 Publisher: Cham Springer International Publishing :Imprint: Birkhäuser


Digital
Constrained Optimization and Optimal Control for Partial Differential Equations
Authors: --- --- --- --- --- et al.
ISBN: 9783034801331 Year: 2012 Publisher: Basel Springer Basel

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Digital
Non-Smooth and Complementarity-Based Distributed Parameter Systems : Simulation and Hierarchical Optimization
Authors: --- --- --- ---
ISBN: 9783030793937 9783030793920 9783030793944 9783030793951 Year: 2022 Publisher: Cham Springer International Publishing :Imprint: Birkhäuser

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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
Constrained Optimization and Optimal Control for Partial Differential Equations
Authors: --- --- --- --- --- et al.
ISBN: 9783034801331 Year: 2012 Publisher: Basel Springer Basel

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This special volume focuses on optimization and control of processes governed by partial differential equations. The contributors are mostly participants of the DFG-priority program 1253: Optimization with PDE-constraints which is active since 2006. The book is organized in sections which cover almost the entire spectrum of modern research in this emerging field. Indeed, even though the field of optimal control and optimization for PDE-constrained problems has undergone a dramatic increase of interest during the last four decades, a full theory for nonlinear problems is still lacking. The contributions of this volume, some of which have the character of survey articles, therefore, aim at creating and developing further new ideas for optimization, control and corresponding numerical simulations of systems of possibly coupled nonlinear partial differential equations. The research conducted within this unique network of groups in more than fifteen German universities focuses on novel methods of optimization, control and identification for problems in infinite-dimensional spaces, shape and topology problems, model reduction and adaptivity, discretization concepts and important applications. Besides the theoretical interest, the most prominent question is about the effectiveness of model-based numerical optimization methods for PDEs versus a black-box approach that uses existing codes, often heuristic-based, for optimization.

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