Linear Network Optimization

The starting point in the formulation of any numerical problem is to take an intuitive idea about the problem in question and to translate it into precise mathematical language. This book provides step-by-step descriptions of how to formulate numerical problems and develops techniques for solving them. A number of engineering case studies motivate the development of efficient algorithms that involve, in some cases, transformation of the problem from its initial formulation into a more tractable form. Five general problem classes are considered: linear systems of equations, non-linear systems of equations, unconstrained optimization, equality-constrained optimization and inequality-constrained optimization. The book contains many worked examples and homework exercises and is suitable for students of engineering or operations research taking courses in optimization. Supplementary material including solutions, lecture slides and appendices are available online at www.cambridge.org/9780521

Finite element methods have become ever more important to engineers as tools for design and optimization, now even for solving non-linear technological problems. However, several aspects must be consi

This text for upper-level undergraduates and graduate students explores stochastic control theory in terms of analysis, parametric optimization, and optimal stochastic control. Limited to linear syste

Lau (McGill University) collects Java procedures for solving problems that require linear algebra, ordinary and partial differential equations, optimization, parameter estimation, and the special func

Questions that arose from linear programming and combinatorial optimization have been a driving force for modern polytope theory, such as the diameter questions motivated by the desire to understand t

An introduction to linear RF amplifier theory and related concepts is followed by chapters addressing linear power amplifier design; conventional high-efficiency amplifier modes; matching network desi

This user-friendly text offers a thorough introduction to the part of optimization theory that lies between approximation theory and mathematical programming, both linear and nonlinear. Written by two

Optimization techniques are at the core of data science, including data analysis and machine learning. An understanding of basic optimization techniques and their fundamental properties provides important grounding for students, researchers, and practitioners in these areas. This text covers the fundamentals of optimization algorithms in a compact, self-contained way, focusing on the techniques most relevant to data science. An introductory chapter demonstrates that many standard problems in data science can be formulated as optimization problems. Next, many fundamental methods in optimization are described and analyzed, including: gradient and accelerated gradient methods for unconstrained optimization of smooth (especially convex) functions; the stochastic gradient method, a workhorse algorithm in machine learning; the coordinate descent approach; several key algorithms for constrained optimization problems; algorithms for minimizing nonsmooth functions arising in data science; found

Linear and Non-Linear Deformations of Elastic Solids aims to compile the advances in the field of linear and non-linear elasticity through discussion crack, contact, scattering and wave propagation in

This book is intended to be a cookbook for students and researchers to understand the finite element method and optimization methods and couple them to effect shape optimization. The optimization part

This textbook on nonlinear optimization focuses on model building, real world problems, and applications of optimization models to natural and social sciences. Organized into two parts, this book may

Designed for engineers, mathematicians, computer scientists, financial analysts, and anyone interested in using numerical linear algebra, matrix theory, and vector calculus concepts to maximize effici

Computational Intelligence for Multimedia Big Data on the Cloud with Engineering Applications covers timely topics, including the neural network (NN), particle swarm optimization (PSO), evolutionary a

This book deals with averaging dynamics, a paradigmatic example of network based dynamics in multi-agent systems. The book presents all the fundamental results on linear averaging dynamics, proposing

This book presents cutting-edge research contributions that address various aspects of network design, optimization, implementation, and application of cognitive radio technologies. It demonstrates ho

This book provides a comprehensive treatment of the optimal control design and analysis of both linear and nonlinear networked systems without needing the system dynamics and network imperfections. Bo

Provides a modern mathematical approach to the design of communication networks for graduate students, blending control, optimization, and stochastic network theories. A broad range of performance analysis tools are discussed, including important advanced topics that have been made accessible to students for the first time. Taking a top-down approach to network protocol design, the authors begin with the deterministic model and progress to more sophisticated models. Network algorithms and protocols are tied closely to the theory, illustrating the practical engineering applications of each topic. The background behind the mathematical analyses is given before the formal proofs and is supported by worked examples, enabling students to understand the big picture before going into the detailed theory. End-of-chapter problems cover a range of difficulties, with complex problems broken into several parts, and hints to many problems are provided to guide students. Full solutions are available

Beginning with the basic concepts of vector spaces such as linear independence, basis and dimension, quotient space, linear transformation and duality with an exposition of the theory of linear operat

Finite-dimensional optimization problems occur throughout the mathematical sciences. The majority of these problems cannot be solved analytically. This introduction to optimization attempts to strike

This book is about optimization techniques and is subdivided into two parts. In the first part a wide overview on optimization theory is presented. Optimization is presented as being composed of five

This book covers the material of an introductory course in linear algebra. Topics include sets and maps, vector spaces, bases, linear maps, matrices, determinants, systems of linear equations, Euclide

"Comprehensively covers the planning, rolling out and optimization of LTE/SAE networks. A hands-on description of the complete end-to-end functionality, network planning and physical construction of L

Cross-layer design seeks to enhance the capacity of wireless networks significantly through the joint optimization of multiple layers in the network, primarily the physical (PHY) and medium access con

This book, written by a leader in neural network theory in Russia, uses mathematical methods in combination with complexity theory, nonlinear dynamics and optimization. It details more than 40 years o

Uniquely blends mathematical theory and algorithm design for understanding and modeling real-world problems Optimization modeling and algorithms are key components to problem-solving across various f

The volume presents a collaboration between internationally recognized experts on anti-optimization and structural optimization, and summarizes various novel ideas, methodologies and results studied

Structural Optimization is intended to supplement the engineer's box of analysis and design tools making optimization as commonplace as the finite element method in the engineering workplace. It begi

Contributors from around the world investigate dimensions of WiMAX network performance, providing information for a professional, technical, and academic audience interested in network planning and op

Nowadays constraint satisfaction problems (CSPs) are ubiquitous in many different areas of computer science, from artificial intelligence and database systems to circuit design, network optimization,

This book, written by a leader in neural network theory in Russia, uses mathematical methods in combination with complexity theory, nonlinear dynamics and optimization. It details more than 40 years o

This self-contained textbook is an informal introduction to optimization through the use of numerous illustrations and applications. The focus is on analytically solving optimization problems with a f

Cross-layer design seeks to enhance the capacity of wireless networks significantly through the joint optimization of multiple layers in the network, primarily the physical (PHY) and medium access con

Neural network research often builds on the fiction that neurons are simple linear threshold units, completely neglecting the highly dynamic and complex nature of synapses, dendrites, and voltage-depe

Yang (California State University) explains complex technology in terms of its basic concepts and offers advice on the design, optimization, and management of a CDMA2000 wireless network. This book co

This concise, undergraduate-level text focuses on combinatorics, graph theory with applications to some standard network optimization problems, and algorithms. Geared toward mathematics and computer s

Every student of mathematics needs a sound grounding in the techniques of linear algebra. It forms the basis of the study of linear equations, matrices, linear mappings, and differential equations, an

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.