Linear Network Optimization

Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and

New edition of a graduate-level textbook on that focuses on online convex optimization, a machine learning framework that views optimization as a process.In many practical applications, the environment is so complex that it is not feasible to lay out a comprehensive theoretical model and use classical algorithmic theory and/or mathematical optimization. Introduction to Online Convex Optimization presents a robust machine learning approach that contains elements of mathematical optimization, game theory, and learning theory: an optimization method that learns from experience as more aspects of the problem are observed. This view of optimization as a process has led to some spectacular successes in modeling and systems that have become part of our daily lives. Based on the “Theoretical Machine Learning” course taught by the author at Princeton University, the second edition of this widely used graduate level text features:Thoroughly updated material throughoutNew chapters on boosting, ad

Based on course-tested material, this rigorous yet accessible graduate textbook covers both fundamental and advanced optimization theory and algorithms. It covers a wide range of numerical methods and topics, including both gradient-based and gradient-free algorithms, multidisciplinary design optimization, and uncertainty, with instruction on how to determine which algorithm should be used for a given application. It also provides an overview of models and how to prepare them for use with numerical optimization, including derivative computation. Over 400 high-quality visualizations and numerous examples facilitate understanding of the theory, and practical tips address common issues encountered in practical engineering design optimization and how to address them. Numerous end-of-chapter homework problems, progressing in difficulty, help put knowledge into practice. Accompanied online by a solutions manual for instructors and source code for problems, this is ideal for a one- or two-sem

In the last few years, Algorithms for Convex Optimization have revolutionized algorithm design, both for discrete and continuous optimization problems. For problems like maximum flow, maximum matching, and submodular function minimization, the fastest algorithms involve essential methods such as gradient descent, mirror descent, interior point methods, and ellipsoid methods. The goal of this self-contained book is to enable researchers and professionals in computer science, data science, and machine learning to gain an in-depth understanding of these algorithms. The text emphasizes how to derive key algorithms for convex optimization from first principles and how to establish precise running time bounds. This modern text explains the success of these algorithms in problems of discrete optimization, as well as how these methods have significantly pushed the state of the art of convex optimization itself.

In the last few years, Algorithms for Convex Optimization have revolutionized algorithm design, both for discrete and continuous optimization problems. For problems like maximum flow, maximum matching, and submodular function minimization, the fastest algorithms involve essential methods such as gradient descent, mirror descent, interior point methods, and ellipsoid methods. The goal of this self-contained book is to enable researchers and professionals in computer science, data science, and machine learning to gain an in-depth understanding of these algorithms. The text emphasizes how to derive key algorithms for convex optimization from first principles and how to establish precise running time bounds. This modern text explains the success of these algorithms in problems of discrete optimization, as well as how these methods have significantly pushed the state of the art of convex optimization itself.

Linear algebra is something all mathematics undergraduates and many other students, in subjects ranging from engineering to economics, have to learn. The fifth edition of this hugely successful textbook retains the quality of earlier editions while at the same time seeing numerous minor improvements and major additions. The latter include: a new chapter on singular values and singular vectors, including ways to analyze a matrix of data; a revised chapter on computing in linear algebra, with professional-level algorithms and code that can be downloaded for a variety of languages; a new section on linear algebra and cryptography; and a new chapter on linear algebra in probability and statistics. A dedicated and active website also offers solutions to exercises as well as new exercises from many different sources (e.g. practice problems, exams, development of textbook examples), plus codes in MATLAB, Julia, and Python.

Providing the first truly comprehensive overview of Network Tomography - a novel network monitoring approach that makes use of inference techniques to reconstruct the internal network state from external vantage points - this rigorous yet accessible treatment of the fundamental theory and algorithms of network tomography covers the most prominent results demonstrated on real-world data, including identifiability conditions, measurement design algorithms, and network state inference algorithms, alongside practical tools for applying these techniques to real-world network management. It describes the main types of mathematical problems, along with their solutions and properties, and emphasizes the actions that can be taken to improve the accuracy of network tomography. With proofs and derivations introduced in an accessible language for easy understanding, this is an essential resource for professional engineers, academic researchers, and graduate students in network management and netwo

A unique text integrating numerics, mathematics and applications to provide a hands-on approach to using optimization techniques, this mathematically accessible textbook emphasises conceptual understanding and importance of theorems rather than elaborate proofs. It allows students to develop fundamental optimization methods before delving into MATLAB®'s optimization toolbox, and to link MATLAB's results with the results from their own code. Following a practical approach, the text demonstrates several applications, from error-free analytic examples to truss (size) optimization, and 2D and 3D shape optimization, where numerical errors are inevitable. The principle of minimum potential energy is discussed to highlight the deep relationship between engineering and optimization. MATLAB code in every chapter illustrates key concepts and the text demonstrates the coupling between MATLAB and SOLIDWORKS® for design optimization. A wide variety of optimization problems are covered including con

Discover the subject of optimization in a new light with this modern and unique treatment. Includes a thorough exposition of applications and algorithms in sufficient detail for practical use, while providing you with all the necessary background in a self-contained manner. Features a deeper consideration of optimal control, global optimization, optimization under uncertainty, multiobjective optimization, mixed-integer programming and model predictive control. Presents a complete coverage of formulations and instances in modelling where optimization can be applied for quantitative decision-making. As a thorough grounding to the subject, covering everything from basic to advanced concepts and addressing real-life problems faced by modern industry, this is a perfect tool for advanced undergraduate and graduate courses in chemical and biochemical engineering.

This introductory text on the subject of linear algebra stresses finite dimensional vector spaces and linear transformations. Proofs are given in detail, and carefully chosen problems demonstrate the

Based on the recommendations of the Linear Algebra Curriculum Study Group, this introduction to linear algebra offers a matrix-oriented approach with more emphasis on problem solving and applications.

A comprehensive introduction to optimization with a focus on practical algorithms for the design of engineering systems.This book offers a comprehensive introduction to optimization with a focus on pr

Linear algebra and the foundations of deep learning, together at last! From Professor Gilbert Strang, acclaimed author of Introduction to Linear Algebra, comes Linear Algebra and Learning from Data, t

Noisy optimization is a topic of growing interest for researchers working on mainstream optimization problems. Although several techniques for dealing with stochastic noise in optimization problems ar

Advances in training models with log-linear structures, with topics including variable selection, the geometry of neural nets, and applications.Log-linear models play a key role in modern big data and

This book presents tools and methods for large-scale and distributed optimization. Since many methods in "Big Data" fields rely on solving large-scale optimization problems, often in distributed fashi

Optimization methods play a central role in financial modeling. This textbook is devoted to explaining how state-of-the-art optimization theory, algorithms, and software can be used to efficiently solve problems in computational finance. It discusses some classical mean–variance portfolio optimization models as well as more modern developments such as models for optimal trade execution and dynamic portfolio allocation with transaction costs and taxes. Chapters discussing the theory and efficient solution methods for the main classes of optimization problems alternate with chapters discussing their use in the modeling and solution of central problems in mathematical finance. This book will be interesting and useful for students, academics, and practitioners with a background in mathematics, operations research, or financial engineering. The second edition includes new examples and exercises as well as a more detailed discussion of mean–variance optimization, multi-period models, and add

Linear and Non-Linear Stability Analysis in Boiling Water Reactors: The Design of Real-Time Stability Monitors presents a thorough analysis of the most innovative BWR reactors and stability phenomena

Offering a clear set of workable examples with data and explanations, Interaction Effects in Linear and Generalized Linear Models is a comprehensive and accessible text that provides a unified approac

This book presents an introduction to optimization, offering the reader the fundamentals of several methods with accompanying practical engineering applications. It includes optimization calculations

Damodar N. Gujarati’s Linear Regression: A Mathematical Introduction presents linear regression theory in a rigorous, but approachable manner that is accessible to students in all social science

A metaheuristic is a consistent set of ideas, concepts, and operators to design a heuristic optimization algorithm, that can provide a sufficiently good solution to an optimization problem with incomp

Energy Optimization in Process Systems and Fuel Cells, Third Edition covers the optimization and integration of energy systems, with a particular focus on fuel cell technology. With rising energy pric

This book presents basic optimization principles and gradient-based algorithms to a general audience, in a brief and easy-to-read form. It enables professionals to apply optimization theory to enginee

An Application-Oriented Introduction to Essential Optimization Concepts and Best Practices Optimization is an inherent human tendency that gained new life after the advent of calculus; now, as the wor

Offering the most geometric presentation available, Linear Algebra with Applications, Fifth Edition emphasizes linear transformations as a unifying theme. This elegant textbook combines a user-friendl

●Introduces central topics, such as vector spaces, linear maps, linear dependence, and eigenvalues, early in the book with the aim of helping students transition from calculus to rigorous mathematics●

A fully updated textbook on linear systems theoryLinear systems theory is the cornerstone of control theory and a well-established discipline that focuses on linear differential equations from the pe

This book combines a solid theoretical background in linear algebra with practical algorithms for numerical solution of linear algebra problems. Developed from a number of courses taught repeatedly by

Elementary Linear Algebra is written for the first undergraduate course. The book focuses on the importance of linear algebra in many disciplines such as engineering, economics, statistics, and comput

Linear Algebra with Applications, Ninth Edition is designed for the introductory course in linear algebra for students within engineering, mathematics, business management, and physics. Updated to inc

This self-contained introduction to numerical linear algebra provides a comprehensive, yet concise, overview of the subject. It includes standard material such as direct methods for solving linear systems and least-squares problems, error, stability and conditioning, basic iterative methods and the calculation of eigenvalues. Later chapters cover more advanced material, such as Krylov subspace methods, multigrid methods, domain decomposition methods, multipole expansions, hierarchical matrices and compressed sensing. The book provides rigorous mathematical proofs throughout, and gives algorithms in general-purpose language-independent form. Requiring only a solid knowledge in linear algebra and basic analysis, this book will be useful for applied mathematicians, engineers, computer scientists, and all those interested in efficiently solving linear problems.

This self-contained introduction to numerical linear algebra provides a comprehensive, yet concise, overview of the subject. It includes standard material such as direct methods for solving linear systems and least-squares problems, error, stability and conditioning, basic iterative methods and the calculation of eigenvalues. Later chapters cover more advanced material, such as Krylov subspace methods, multigrid methods, domain decomposition methods, multipole expansions, hierarchical matrices and compressed sensing. The book provides rigorous mathematical proofs throughout, and gives algorithms in general-purpose language-independent form. Requiring only a solid knowledge in linear algebra and basic analysis, this book will be useful for applied mathematicians, engineers, computer scientists, and all those interested in efficiently solving linear problems.

Nanoscale Fabrication, Optimization, Scale-up and Biological Aspects of Pharmaceutical Nanotechnology focuses on the fabrication, optimization, scale-up and biological aspects of pharmaceutical nanote

This book discusses the major aspects of load flow, optimization, optimal load flow, and culminates in modern heuristic optimization techniques and evolutionary programming. In the deregulated environ

A comprehensive resource containing the operating principles and key insights of LTE networks performance optimization LTE Optimization Engineering Handbook is a comprehensive reference that desc

Concise Introduction to Linear Algebra deals with the subject of linear algebra, covering vectors and linear systems, vector spaces, orthogonality, determinants, eigenvalues and eigenvectors, singular

This book presents a systematic overview of approximation by linear combinations of positive linear operators, a useful tool used to increase the order of approximation. Fundamental and recent results

This advanced graduate-level treatment of semigroup theory explores semigroups of linear operators and linear Cauchy problems. The author emphasizes motivation and heuristics as well as applications.

This book offers an introduction to numerical optimization methods in structural design. Employing a readily accessible and compact format, the book presents an overview of optimization methods, and e