Stochastic Recursive Algorithms for Optimization

Stochastic Recursive Algorithms for Optimization presents algorithms for constrained and unconstrained optimization and for reinforcement learning. Efficient perturbation approaches form a thread unif

This book presents a thorough development of the modern theory of stochastic approximation or recursive stochastic algorithms for both constrained and unconstrained problems. This second edition is a

Authoritative coverage of a revolutionary technique for overcoming problems in electromagnetic design Genetic algorithms are stochastic search procedures modeled on the Darwinian concepts of natural s

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

This book summarizes developments related to a class of methods called Stochastic Decomposition (SD) algorithms, which represent an important shift in the design of optimization algorithms. Unlike tra

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

Based on the author's forty years of teaching experience, this unique textbook covers both basic and advanced concepts of optimization theory and methods for process systems engineers. Topics covered include continuous, discrete and logic optimization (linear, nonlinear, mixed-integer and generalized disjunctive programming), optimization under uncertainty (stochastic programming and flexibility analysis), and decomposition techniques (Lagrangean and Benders decomposition). Assuming only a basic background in calculus and linear algebra, it enables easy understanding of mathematical reasoning, and numerous examples throughout illustrate key concepts and algorithms. End-of-chapter exercises involving theoretical derivations and small numerical problems, as well as in modeling systems like GAMS, enhance understanding and help put knowledge into practice. Accompanied by two appendices containing web links to modeling systems and models related to applications in PSE, this is an essential

This simple, compact toolkit for designing and analyzing stochastic approximation algorithms requires only basic literacy in probability and differential equations. Yet these algorithms have powerful applications in control and communications engineering, artificial intelligence and economic modelling. The dynamical systems viewpoint treats an algorithm as a noisy discretization of a limiting differential equation and argues that, under reasonable hypotheses, it tracks the asymptotic behaviour of the differential equation with probability one. The differential equation, which can usually be obtained by inspection, is easier to analyze. Novel topics include finite-time behaviour, multiple timescales and asynchronous implementation. There is a useful taxonomy of applications, with concrete examples from engineering and economics. Notably it covers variants of stochastic gradient-based optimization schemes, fixed-point solvers, which are commonplace in learning algorithms for approximate

This title offers a framework for online decision making under uncertainty and time constraints, with online stochastic algorithms for implementing the framework, performance guarantees, and demonstra

This book presents a thorough development of the modern theory of stochastic approximation or recursive stochastic algorithms for both constrained and unconstrained problems. This second edition is a

Macroeconomics offers a modern and comprehensive introduction to the tools and methods that define contemporary graduate training in the field. Written for first-year PhD students and advanced MA/MS students, the book provides a rigorous yet accessible foundation in dynamic optimization, recursive methods, competitive equilibrium, stochastic modelling, and welfare analysis. It emphasizes clarity and intuition, guiding readers through the logic of intertemporal decision-making that underlies modern macro theory. A key feature of the text is its explicit connection to data. Throughout the book, theory is used to interpret empirical patterns, illustrating how macroeconomic models help us understand real-world behavior and policy-relevant facts. Quantitative and computational tools are integrated throughout to show how models are taken to the data. The book develops frameworks with heterogeneity and frictions, including incomplete markets, borrowing constraints, labor-market search frictio