From the Euclidean Space and the Circle to Lie Groups
Coordination, consensus, and synchronization are found in diverse natural phenomena and engineering applications. Examples are flocking birds, illuminating fireflies, a school of fish, and distributed control and sensing. The simplest of such problems are set in the Euclidean spaces and the circle. Consensus and Synchronization: From the Euclidean ......
This book is a self-contained introduction to quantum algorithms with an emphasis on quantum optimization, that is, quantum algorithms to solve optimization problems. The book provides all the tools necessary to understand the benefits and drawbacks of quantum optimization algorithms, paying particular attention to provable guarantees and ......
The shape of the Earth was a significant scientific question in the eighteenth century. When it was discovered that the Earth was flattened at the poles, scientists sought to understand the cause, leading to the study of the gravitational attraction of celestial spheroids. The solution drew upon Newton's law of universal gravitation, which used ......
This book addresses an important class of problems in the field of mathematical optimization- - those involving nonconvex and/or nonsmooth continuous functions. The authors introduce the theoretical foundations of nonconvex nonsmooth functions and discuss optimality conditions for optimization problems involving such functions. They also provide ......
And Related Problems of Mathematical Physics, Engineering, and Life Sciences
This book is the first to offer a systematic methodology for solving nonlinear ordinary differential equations (ODEs) using power series, specifically those arising in mathematical physics. It provides tools to eliminate the tedious manipulation of infinite series, enabling recursive computation of all terms. The authors also present a structured ......
Conditional Gradient Methods: From Core Principles to AI Applications offers a definitive and modern treatment of one of the most elegant and versatile algorithmic families in optimization: the Frank-Wolfe method and its many variants. Originally proposed in the 1950s, these projection-free techniques have seen a powerful resurgence, now playing a ......
This book analyzes a variety of results related to the modeling, analysis, estimation, and control design and the applications of different configurations of tubular reactors of two classes of partial differential equations (hyperbolic and parabolic), both linear and nonlinear. The advantages of using the tubular reactor case to study distributed ......
Research on the Anderson Acceleration (AA) has exploded in the last 15 years. This book brings together these recent fundamental results applied to nonlinear solvers for PDEs, which are ubiquitous across mathematics, science, engineering, and economics as predictive models for a vast quantity of important phenomena. Coverage includes: AA ......
This comprehensive book focuses on numerical methods for approximating solutions to partial differential equations. Intended as a broad survey of methods, the aim is to introduce readers to the central concepts of various families of discretizations and solution algorithm and lay the foundation needed to understand more advanced material, The book ......
