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 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 ......
Using material from many different sources in a systematic and unified way, this self-contained book provides both rigorous mathematical theory and practical numerical insights while developing a framework for determining the convergence rate of discrete approximations to optimal control problems. Elements of the framework include the reference ......
This self-contained textbook provides the foundations of linear optimization, covering topics in both continuous and discrete linear optimization. It gradually builds the connection between theory, algorithms, and applications so that readers gain a theoretical and algorithmic foundation, familiarity with a variety of applications, and the ability ......
Most books on algorithms are narrowly focused on a single field of application. This unique book cuts across discipline boundaries, exposing readers to the most successful algorithms from a variety of fields. Algorithm derivation is a legitimate branch of the mathematical sciences driven by hardware advances and the demands of many scientific ......
A Comprehensive Introduction to Modeling, Analysis, Simulation, Applications
Historically, optimal transport was about moving a pile of mortar efficiently or transferring the output of an array of steel mines optimally. This type of problem has been found to arise in many different fields of mathematics, science, and engineering-from fluid dynamics to many-electron physics to artificial intelligence-and in the last three ......
The method of least squares, discovered by Gauss in 1795, is a principal tool for reducing the influence of errors when fitting a mathematical model to given observations. Applications arise in a great number of areas in sciences and engineering. The increased use of automatic data capturing frequently leads to large-scale least squares problems. ......
Set-valued, convex, and nonsmooth analysis are relatively modern branches of mathematical analysis and increasingly relevant in current control theory and control engineering literature. The first book of this scope and at this level, Set-Valued, Convex, and Nonsmooth Analysis in Dynamics and Control serves as a broad introduction to the field and ......
The only book offering solved exercises for integer and combinatorial optimization, this book contains 102 classroom tested problems of varying scope and difficulty chosen from a plethora of topics and applications. It has an associated website containing additional problems, miscellaneous material including suggested readings, and errata. Topics ......
