Classical and modern optimization
Carlier, Guillaume.
Classical and modern optimization Guillaume Carlier, Université Paris Dauphine, France. - Singapore: World Scientific, 2024. - xiii, 371p. - Advanced textbooks in mathematics, 2059-769X .
Includes bibliographical references and index.
Topological and functional analytic preliminaries -- Differential calculus -- Convexity -- Optimality conditions for differentiable optimization -- Problems depending on a parameter -- Convex duality and applications -- Iterative methods for convex minimization -- When optimization and data meet -- An invitation to the calculus of variations.
"The quest for the optimal is ubiquitous in nature and human behavior. The field of mathematical optimization has a long history and remains active today, particularly in the development of machine learning. Classical and Modern Optimization presents a self-contained overview of classical and modern ideas and methods in approaching optimization problems. The approach is rich and flexible enough to address smooth and non-smooth, convex and non-convex, finite or infinite-dimensional, static or dynamic situations. The first chapters of the book are devoted to the classical toolbox: topology and functional analysis, differential calculus, convex analysis and necessary conditions for differentiable constrained optimization. The remaining chapters are dedicated to more specialized topics and applications. Valuable to a wide audience, including students in mathematics, engineers, data scientists or economists, Classical and Modern Optimization contains more than 200 exercises to assist with self-study or for anyone teaching a third- or fourth-year optimization class"--
9781944660529 (Pbk)
2021028030
Mathematical optimization.
QA402.5
519.6 C194C
Classical and modern optimization Guillaume Carlier, Université Paris Dauphine, France. - Singapore: World Scientific, 2024. - xiii, 371p. - Advanced textbooks in mathematics, 2059-769X .
Includes bibliographical references and index.
Topological and functional analytic preliminaries -- Differential calculus -- Convexity -- Optimality conditions for differentiable optimization -- Problems depending on a parameter -- Convex duality and applications -- Iterative methods for convex minimization -- When optimization and data meet -- An invitation to the calculus of variations.
"The quest for the optimal is ubiquitous in nature and human behavior. The field of mathematical optimization has a long history and remains active today, particularly in the development of machine learning. Classical and Modern Optimization presents a self-contained overview of classical and modern ideas and methods in approaching optimization problems. The approach is rich and flexible enough to address smooth and non-smooth, convex and non-convex, finite or infinite-dimensional, static or dynamic situations. The first chapters of the book are devoted to the classical toolbox: topology and functional analysis, differential calculus, convex analysis and necessary conditions for differentiable constrained optimization. The remaining chapters are dedicated to more specialized topics and applications. Valuable to a wide audience, including students in mathematics, engineers, data scientists or economists, Classical and Modern Optimization contains more than 200 exercises to assist with self-study or for anyone teaching a third- or fourth-year optimization class"--
9781944660529 (Pbk)
2021028030
Mathematical optimization.
QA402.5
519.6 C194C