An Introduction to Convexity, Optimization, and Algorithms by Heinz H. Bauschke and Walaa M. Moursi is a concise 2023 textbook that develops the mathematical foundations of convex analysis and optimization and then connects them directly to computational algorithms. It begins with affine and convex sets, convex and lower-semicontinuous functions, minimizers, support functions, projections, subgradients, normal cones, derivatives, and duality. The later chapters move toward optimality conditions such as the Karush–Kuhn–Tucker conditions, Fenchel–Rockafellar duality, and smoothness/Lipschitz continuity.
The central theme is turning this theory into practical optimization methods. The book develops algorithms including the proximal-gradient method, FISTA (fast iterative soft-thresholding), Douglas–Rachford, and Peaceman–Rachford splitting, with Julia examples and more than 200 exercises.
These methods are particularly relevant to modern computational mathematics, machine learning, signal processing, image reconstruction, and data science. Overall, the book serves as a bridge between rigorous mathematical convex analysis and the algorithms used to solve large-scale optimization problems.
BOOK
The central theme is turning this theory into practical optimization methods. The book develops algorithms including the proximal-gradient method, FISTA (fast iterative soft-thresholding), Douglas–Rachford, and Peaceman–Rachford splitting, with Julia examples and more than 200 exercises.
These methods are particularly relevant to modern computational mathematics, machine learning, signal processing, image reconstruction, and data science. Overall, the book serves as a bridge between rigorous mathematical convex analysis and the algorithms used to solve large-scale optimization problems.
BOOK
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