Convex Analysis and Monotone Operator Theory in Hilbert Spaces
by Heinz H. Bauschke · first published 2011
2mentions
2recommended by
2HN commenters
2018–2021first – last mentioned
100% recommend
This book presents a largely self-contained account of the main results of convex analysis, monotone operator theory, and the theory of nonexpansive operators in the context of Hilbert spaces. Unlike existing literature, the novelty of this book, and indeed its central theme, is the tight interplay among the key notions of convexity, monotonicity, and nonexpansiveness. The presentation is accessible to a broad audience and attempts to reach out in particular to the applied sciences and engineering communities, where these tools have become indispensable. Graduate students and researchers in
Affiliate links. As an Amazon Associate I earn from qualifying purchases.
…(1982), but provides a solid foundation - "Convex Optimization" by S. Boyd and L. Vandenberghe: the standard for learning convex optimization (also available as a free PDF from the author's website) - "Convex Analysis and Monotone Operator Theory in Hilbert Spaces" by H. H. Bauschke and P. L. Combettes: covers a more specialized area of numerical optimization, but the notation is beautiful (IMO) and it acts as a useful reference for recent research on, e.g., operator…
on “Ask HN: What are the best textbooks in your field of expertise?” ↗…give a lecture for a course. [0] https://web.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf Convex Optimization, Boyd and Vandenberghe [1] An Introduction to Multivariate Statistical Analysis, Anderson [2] Convex Analysis and Monotone Operator Theory in Hilbert Spaces, Bauschke-Combettes [3] Theory of Multivariate Statistics, Bilodeau-Brenner [4] The Elements of Integration and Lebesgue Measure, Bartle [5] Probability: Theory and Examples, Durrett
on “The Modern Mathematics of Deep Learning” ↗