Carlier, Guillaume
Classical and Modern Optimization - New Jersey World Scientific 2023 - xiii, 371p.
1. Topological and functional analytic preliminaries
2. Differential calculus
3. Convexity
4. Optimality conditions for differentiable optimization
5. Problems depending on a parameter
6. Convex duality and applications
7. Iterative methods for convex minimization
8. When optimization and data meet
9. 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 (PB)
Mathematical Optimization
Convexity
Calculus of Variations
517 / CAR
Classical and Modern Optimization - New Jersey World Scientific 2023 - xiii, 371p.
1. Topological and functional analytic preliminaries
2. Differential calculus
3. Convexity
4. Optimality conditions for differentiable optimization
5. Problems depending on a parameter
6. Convex duality and applications
7. Iterative methods for convex minimization
8. When optimization and data meet
9. 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 (PB)
Mathematical Optimization
Convexity
Calculus of Variations
517 / CAR