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This work is intended to serve as a guide for graduate students and researchers who wish to get acquainted with the main theoretical and practical tools for the numerical minimization of convex functions on Hilbert spaces. Therefore, it contains the main tools that are necessary to conduct independent research on the topic. It is also a concise, easy-to-follow and self-contained textbook, which may be useful for any researcher working on related fields, as well as teachers giving graduate-level courses on the topic. It will contain a thorough revision of the extant literature including both classical and state-of-the-art references.

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Basic Functional Analysis.- Existence of Minimizers.- Convex Analysis and Subdifferential Calculus.- Examples.- Problem-solving Strategies.- Keynote Iterative Methods.

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"This short book is dedicated to convex optimization, beginning with theoretical aspects, ending with numerical methods, and complemented with numerous examples. ... this is an interesting and well-written book that is adequate for a graduate-level course on convex optimization." (Constantin Zalinescu, Mathematical Reviews, November, 2015)

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Juan Peypouquet is an Associate Professor at the Mathematics Department of the Universidad Tecnica Federico Santa Maria. His main research interest is the study of the asymptotic behavior of dynamical systems in a broad sense, along with their applications in variational analysis and optimization.

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