Implicit filtering is a way to solve bound-constrained optimization problems for which derivative information is not available. Unlike methods that use interpolation to reconstruct the function and its higher derivatives, implicit filtering builds upon coordinate search and then interpolates to get an approximation of the gradient. The author describes the algorithm, its convergence theory, and a new MATLAB implementation, and includes three case studies. This book is unique in that it is the only one in the area of derivative-free or sampling methods and is accompanied by publicly available software. It is also designed as a software manual and as a reference for implicit filtering - one can approach the book as a consumer of the software, as a student, or as a researcher in sampling and derivative-free methods. The book includes a chapter on convergence theory that is both accessible to students and an overview of recent results on optimization of noisy functions, including results that depend on non-smooth analysis and results on the handling of constraints. Implicit filtering is used in applications in electrical, civil, and mechanical engineering.

This book dives into the inner workings of recommender systems, those ubiquitous technologies that shape our online experiences. From Netflix show suggestions to personalized product recommendations on Amazon or the endless stream of curated YouTube videos, these systems power the choices we see every day. Collaborative filtering reigns supreme as the dominant approach behind recommender systems. This book offers a comprehensive exploration of this topic, starting with memory-based techniques. These methods, known for their ease of understanding and implementation, provide a solid foundation for understanding collaborative filtering. As you progress, you’ll delve into latent factor models, the abstract and mathematical engines driving modern recommender systems. The journey continues with exploring the concepts of metadata and diversity. You’ll discover how metadata, the additional information gathered by the system, can be harnessed to refine recommendations. Additionally, the book delves into techniques for promoting diversity, ensuring a well-balanced selection of recommendations. Finally, the book concludes with a discussion of cutting-edge deep learning models used in recommender systems. This book caters to a dual audience. First, it serves as a primer for practicing IT professionals or data scientists eager to explore the realm of recommender systems. The book assumes a basic understanding of linear algebra and optimization but requires no prior knowledge of machine learning or programming. This makes it an accessible read for those seeking to enter this exciting field. Second, the book can be used as a textbook for a graduate-level course. To facilitate this, the final chapter provides instructors with a potential course plan.

System Modeling and Optimization XX deals with new developments in the areas of optimization, optimal control and system modeling. The themes range across various areas of optimization: continuous and discrete, numerical and analytical, finite and infinite dimensional, deterministic and stochastic, static and dynamic, theory and applications, foundations and case studies. Besides some classical topics, modern areas are also presented in the contributions, including robust optimization, filter methods, optimization of power networks, data mining and risk control. This volume contains invited and selected papers from presentations at the 20th IFIP TC7 Conference on System Modeling and Optimization, which took place at the University of Trier, Germany from July 23 to 27, 2001, and which was sponsored by the International Federation for Information Processing (IFIP).

Publisher Description

Keywords: water resources, implicit filtering, stochastic simulation, variance reduction, noisy functions, optimization.

Model reduction and coarse-graining are important in many areas of science and engineering. How does a system with many degrees of freedom become one with fewer? How can a reversible micro-description be adapted to the dissipative macroscopic model? These crucial questions, as well as many other related problems, are discussed in this book. All contributions are by experts whose specialities span a wide range of fields within science and engineering.

Advanced Approaches in Turbulence: Theory, Modeling, Simulation and Data Analysis for Turbulent Flows focuses on the updated theory, simulation and data analysis of turbulence dealing mainly with turbulence modeling instead of the physics of turbulence. Beginning with the basics of turbulence, the book discusses closure modeling, direct simulation, large eddy simulation and hybrid simulation. The book also covers the entire spectrum of turbulence models for both single-phase and multi-phase flows, as well as turbulence in compressible flow. Turbulence modeling is very extensive and continuously updated with new achievements and improvements of the models. Modern advances in computer speed offer the potential for elaborate numerical analysis of turbulent fluid flow while advances in instrumentation are creating large amounts of data. This book covers these topics in great detail. - Covers the fundamentals of turbulence updated with recent developments - Focuses on hybrid methods such as DES and wall-modeled LES - Gives an updated treatment of numerical simulation and data analysis

In financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden & Platen: Numerical Solution of Stochastic Differential Equations (1992). The present monograph builds on the above-mentioned work and provides an introduction to stochastic differential equations with jumps, in both theory and application, emphasizing the numerical methods needed to solve such equations. It presents many new results on higher-order methods for scenario and Monte Carlo simulation, including implicit, predictor corrector, extrapolation, Markov chain and variance reduction methods, stressing the importance of their numerical stability. Furthermore, it includes chapters on exact simulation, estimation and filtering. Besides serving as a basic text on quantitative methods, it offers ready access to a large number of potential research problems in an area that is widely applicable and rapidly expanding. Finance is chosen as the area of application because much of the recent research on stochastic numerical methods has been driven by challenges in quantitative finance. Moreover, the volume introduces readers to the modern benchmark approach that provides a general framework for modeling in finance and insurance beyond the standard risk-neutral approach. It requires undergraduate background in mathematical or quantitative methods, is accessible to a broad readership, including those who are only seeking numerical recipes, and includes exercises that help the reader develop a deeper understanding of the underlying mathematics.

See report.

This volume contains six keynote lectures and 44 contributed papers of the TI 2009 conference that was held in Saint-Luce, La Martinique, May 31-June 5, 2009. These lectures address the latest developments in direct numerical simulations, large eddy simulations, compressible turbulence, coherent structures, droplets, two-phase flows, etc. The present monograph is a snapshot of the state-of-the-art in the field of turbulence with a broad view on theory, experiments and numerical simulations.