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Recent Advances in Optimization and its Applications in Engineering
Mathematical optimization encompasses both a rich and rapidly evolving body of fundamental theory, and a variety of exciting applications in science and engineering. The present book contains a careful selection of articles on recent advances in optimization theory, numerical methods, and their applications in engineering. It features in particular new methods and applications in the fields of optimal control, PDE-constrained optimization, nonlinear optimization, and convex optimization. The authors of this volume took part in the 14th Belgian-French-German Conference on Optimization (BFG09) organized in Leuven, Belgium, on September 14-18, 2009. The volume contains a selection of reviewed articles contributed by the conference speakers as well as three survey articles by plenary speakers and two papers authored by the winners of the best talk and best poster prizes awarded at BFG09. Researchers and graduate students in applied mathematics, computer science, and many branches of engineering will find in this book an interesting and useful collection of recent ideas on the methods and applications of optimization.
Advances in Energy System Optimization
The papers presented in this volume address diverse challenges in energy systems, ranging from operational to investment planning problems, from market economics to technical and environmental considerations, from distribution grids to transmission grids and from theoretical considerations to data provision concerns and applied case studies. The International Symposium on Energy System Optimization (ISESO) was held on November 9th and 10th 2015 at the Heidelberg Institute for Theoretical Studies (HITS) and was organized by HITS, Heidelberg University and Karlsruhe Institute of Technology.
Self-Regularity
Research on interior-point methods (IPMs) has dominated the field of mathematical programming for the last two decades. Two contrasting approaches in the analysis and implementation of IPMs are the so-called small-update and large-update methods, although, until now, there has been a notorious gap between the theory and practical performance of these two strategies. This book comes close to bridging that gap, presenting a new framework for the theory of primal-dual IPMs based on the notion of the self-regularity of a function. The authors deal with linear optimization, nonlinear complementarity problems, semidefinite optimization, and second-order conic optimization problems. The framework a...
Evaluation and Decision Models
1. 1 Motivations Deciding is a very complex and difficult task. Some people even argue that our ability to make decisions in complex situations is the main feature that distinguishes us from animals (it is also common to say that laughing is the main difference). Nevertheless, when the task is too complex or the interests at stake are too important, it quite often happens that we do not know or we are not sure what to decide and, in many instances, we resort to a decision support technique: an informal one-we toss a coin, we ask an oracle, we visit an astrologer, we consult an expert, we think-or a formal one. Although informal decision support techniques can be of interest, in this book, we...
Nonnegative Matrix Factorization
Nonnegative matrix factorization (NMF) in its modern form has become a standard tool in the analysis of high-dimensional data sets. This book provides a comprehensive and up-to-date account of the most important aspects of the NMF problem and is the first to detail its theoretical aspects, including geometric interpretation, nonnegative rank, complexity, and uniqueness. It explains why understanding these theoretical insights is key to using this computational tool effectively and meaningfully. Nonnegative Matrix Factorization is accessible to a wide audience and is ideal for anyone interested in the workings of NMF. It discusses some new results on the nonnegative rank and the identifiability of NMF and makes available MATLAB codes for readers to run the numerical examples presented in the book. Graduate students starting to work on NMF and researchers interested in better understanding the NMF problem and how they can use it will find this book useful. It can be used in advanced undergraduate and graduate-level courses on numerical linear algebra and on advanced topics in numerical linear algebra and requires only a basic knowledge of linear algebra and optimization.
The Joint Spectral Radius
This monograph is based on the Ph.D. Thesis of the author [58]. Its goal is twofold: First, it presents most researchwork that has been done during his Ph.D., or at least the part of the work that is related with the joint spectral radius. This work was concerned with theoretical developments (part I) as well as the study of some applications (part II). As a second goal, it was the author’s feeling that a survey on the state of the art on the joint spectral radius was really missing in the literature, so that the ?rst two chapters of part I present such a survey. The other chapters mainly report personal research, except Chapter 5 which presents animportantapplicationofthejointspectralradi...
Algorithms and Dynamical Models for Communities and Reputation in Social Networks
A persistent problem when finding communities in large complex networks is the so-called resolution limit. This thesis addresses this issue meticulously, and introduces the important notion of resolution-limit-free. Remarkably, only few methods possess this desirable property, and this thesis puts forward one such method. Moreover, it discusses how to assess whether communities can occur by chance or not. One aspect that is often ignored in this field is treated here: links can also be negative, as in war or conflict. Besides how to incorporate this in community detection, it also examines the dynamics of such negative links, inspired by a sociological theory known as social balance. This has intriguing connections to the evolution of cooperation, suggesting that for cooperation to emerge, groups often split in two opposing factions. In addition to these theoretical contributions, the thesis also contains an empirical analysis of the effect of trading communities on international conflict, and how communities form in a citation network with positive and negative links.
Regularization, Optimization, Kernels, and Support Vector Machines
Regularization, Optimization, Kernels, and Support Vector Machines offers a snapshot of the current state of the art of large-scale machine learning, providing a single multidisciplinary source for the latest research and advances in regularization, sparsity, compressed sensing, convex and large-scale optimization, kernel methods, and support vector machines. Consisting of 21 chapters authored by leading researchers in machine learning, this comprehensive reference: Covers the relationship between support vector machines (SVMs) and the Lasso Discusses multi-layer SVMs Explores nonparametric feature selection, basis pursuit methods, and robust compressive sensing Describes graph-based regular...
LATIN 2008: Theoretical Informatics
This book constitutes the refereed proceedings of the 8th International Latin American Symposium on Theoretical Informatics, LATIN 2008, held in Búzios, Brazil, in April 2008. The 66 revised full papers presented together with the extended abstract of 1 invited paper were carefully reviewed and selected from 242 submissions. The papers address a veriety of topics in theoretical computer science with a certain focus on algorithms, automata theory and formal languages, coding theory and data compression, algorithmic graph theory and combinatorics, complexity theory, computational algebra, computational biology, computational geometry, computational number theory, cryptography, theoretical aspects of databases and information retrieval, data structures, networks, logic in computer science, machine learning, mathematical programming, parallel and distributed computing, pattern matching, quantum computing and random structures.
Trust Region Methods
This is the first comprehensive reference on trust-region methods, a class of numerical algorithms for the solution of nonlinear convex optimization methods. Its unified treatment covers both unconstrained and constrained problems and reviews a large part of the specialized literature on the subject. It also provides an up-to-date view of numerical optimization.
