Volume 2 applies the linear algebra concepts presented in Volume 1 to optimization problems which frequently occur throughout machine learning. This book blends theory with practice by not only carefully discussing the mathematical under pinnings of each optimization technique but by applying these techniques to linear programming, support vector machines (SVM), principal component analysis (PCA), and ridge regression. Volume 2 begins by discussing preliminary concepts of optimization theory suc...
The first volume, Geometry, Language and Strategy, extended the concepts of Game Theory, replacing static equilibrium with a deterministic dynamic theory. The first volume opened up many applications that were only briefly touched on. To study the consequences of the deterministic approach in contrast to standard Bayesian approaches, the richness of applications, requires an engineering foundation and discipline, which this volume supplies. It provides a richer list of applications, such as the...
It is fitting that Book I of the series should be on the subject of finite elements. The finite element method is now well established as an engineering tool with wide application. At the same time is has attracted considerable attention from mathematicians over the last ten years, so that a large body of mathematical theory now exists.
Real And Stochastic Analysis: Current Trends
This book presents the current status and research trends in Stochastic Analysis. Several new and emerging research areas are described in detail, highlighting the present outlook in Stochastic Analysis and its impact on abstract analysis. The book focuses on treating problems in areas that serve as a launching pad for continual research.
What is the shortest possible route for a traveling salesman seeking to visit each city on a list exactly once and return to his city of origin? It sounds simple enough, yet the traveling salesman problem is one of the most intensely studied puzzles in applied mathematics--and it has defied solution to this day. In this book, William Cook takes readers on a mathematical excursion, picking up the salesman's trail in the 1800s when Irish mathematician W. R. Hamilton first defined the problem, and...
Multi-Period Trading via Convex Optimization (Foundations and Trends in Optimization)
by Stephen Boyd, Enzo Busseti, Steven Diamond, Ronald N Kahn, and Kwangmoo Koh
Multi-Period Trading via Convex Optimization considers a basic model of multi-period trading, which can be used to evaluate the performance of a trading strategy. It describes a framework for single-period optimization, where the trades in each period are found by solving a convex optimization problem that trades off expected return, risk, transaction cost and holding cost such as the borrowing cost for shorting assets. It then describes a multiperiod version of the trading method, where optimiz...
Nonlinear & Complex Systems
This book aims to provide an overview of the recent research devoted to nonlinear and chaotic systems by discussing the modeling of different phenomena. It will encompass methods and techniques from the analysis of nonlinear ordinary differential equations, perturbation theory, bifurcation analysis and chaos synchronization. It contains 19 chapters, organized into 3 sections:Section 1 - Resonance Phenomena, Nonlinear Vibrations and Waves.Section 2 - Perturbation Theory and Homotopy Perturbation...
Nature-inspired computation is an interdisciplinary topic area that connects the natural sciences to computer science. Since natural computing is utilized in a variety of disciplines, it is imperative to research its capabilities in solving optimization issues. The Handbook of Research on Natural Computing for Optimization Problems discusses nascent optimization procedures in nature-inspired computation and the innovative tools and techniques being utilized in the field. Highlighting empirical r...
Mathematically, most of the interesting optimization problems can be formulated to optimize some objective function, subject to some equality and/or inequality constraints. This book introduces some classical and basic results of optimization theory, including nonlinear programming with Lagrange multiplier method, the Karush-Kuhn-Tucker method, Fritz John's method, problems with convex or quasi-convex constraints, and linear programming with geometric method and simplex method.A slim book such a...
A comprehensive account of the theory and application of Monte Carlo methods Based on years of research in efficient Monte Carlo methods for estimation of rare-event probabilities, counting problems, and combinatorial optimization, Fast Sequential Monte Carlo Methods for Counting and Optimization is a complete illustration of fast sequential Monte Carlo techniques. The book provides an accessible overview of current work in the field of Monte Carlo methods, specifically sequential Monte Carlo te...
Reliability modeling has been a major concern for engineers and managers engaged in high quality system designs. This book presents the recent advancement in reliability theory and reliability engineering.Starting from maintenance policies, the book introduces reliability analysis to systems using stochastic processes to study their optimization problems. In this book, the authors will illustrate how these techniques of reliability are applied to solve optimization problems in computer, informat...
This unique book provides a comprehensive introduction to computational mathematics, which forms an essential part of contemporary numerical algorithms, scientific computing and optimization. It uses a theorem-free approach with just the right balance between mathematics and numerical algorithms. This edition covers all major topics in computational mathematics with a wide range of carefully selected numerical algorithms, ranging from the root-finding algorithm, numerical integration, numerical...
This book consists of a series of new, peer-reviewed papers in stochastic processes, analysis, filtering and control, with particular emphasis on mathematical finance, actuarial science and engineering. Paper contributors include colleagues, collaborators and former students of Robert Elliott, many of whom are world-leading experts and have made fundamental and significant contributions to these areas.This book provides new important insights and results by eminent researchers in the considered...
Ottimizzazione Combinatoria
A UNIQUE ENGINEERING AND STATISTICAL APPROACH TO OPTIMAL RESOURCE ALLOCATION Optimal Resource Allocation: With Practical Statistical Applications and Theory features the application of probabilistic and statistical methods used in reliability engineering during the different phases of life cycles of technical systems. Bridging the gap between reliability engineering and applied mathematics, the book outlines different approaches to optimal resource allocation and various applications of models a...
Topology Optimization in Engineering Structure Design
by Jihong Zhu and Tong Gao
Topology Optimization in Engineering Structure Design explores the recent advances and applications of topology optimization in engineering structures design, with a particular focus on aircraft and aerospace structural systems. To meet the increasingly complex engineering challenges provided by rapid developments in these industries, structural optimization techniques have developed in conjunction with them over the past two decades. The latest methods and theories to improve mechanical perfor...
Six Sigma is a management program that provides tools that help manufacturers obtain efficient, stream-lined production to coincide with ultimate high quality products. Essentials of Lean Six Sigma will show how the well-regarded analytical tools of Six Sigma quality control can be successfully brought into the well-established models of “lean manufacturing, bringing efficient, stream-lined production and high quality product readily together. This book offers a thorough, yet concise introducti...
Topology Design Methods for Structural Optimization
by Osvaldo M. Querin, Mariano Victoria, Cristina Alonso Gordoa, Ruben Ansola, and Pascual Marti
Topology Design Methods for Structural Optimization provides engineers with a basic set of design tools for the development of 2D and 3D structures subjected to single and multi-load cases and experiencing linear elastic conditions. Written by an expert team who has collaborated over the past decade to develop the methods presented, the book discusses essential theories with clear guidelines on how to use them. Case studies and worked industry examples are included throughout to illustrate pr...
Handbook of AI-based Metaheuristics (Advances in Metaheuristics)
At the heart of the optimization domain are mathematical modeling of the problem and the solution methodologies. The problems are becoming larger and with growing complexity. Such problems are becoming cumbersome when handled by traditional optimization methods. This has motivated researchers to resort to artificial intelligence (AI)-based, nature-inspired solution methodologies or algorithms. The Handbook of AI-based Metaheuristics provides a wide-ranging reference to the theoretical and mathe...
Convex Optimization Techniques for Geometric Covering Problems
by Jan Hendrik Rolfes