Fundamentals of Convex Analysis and Optimization

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Fundamentals of Convex Analysis and Optimization
(英文，可编辑的pdf电子文档)

Textbook:Fundamentals of Convex Analysis and Optimization: A Supremum Function Approach
Operations Research and Financial Engineering
Author(s): Rafael Correa, Abderrahim Hantoute, Marco A. López

Course Description:
This course aims at an innovative approach within the framework of convex analysis and optimization, based on an in-depth study of the behavior and properties of the supremum of families of convex functions. It presents an original and systematic treatment of convex analysis, covering standard results and improved calculus rules in subdifferential analysis. The tools supplied in the text allow a direct approach to the mathematical foundations of convex optimization, in particular to optimality and duality theory. Other applications in the book concern convexification processes in optimization, non-convex integration of the Fenchel subdifferential, variational characterizations of convexity, and the study of Chebychev sets. At the same time, the underlying geometrical meaning of all the involved concepts and operations is highlighted and duly emphasized. A notable feature of the book is its unifying methodology, as well as the novelty of providing an alternative or complementary view to the traditional one in which the discipline is presented to students and researchers.



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关键词：Optimization Fundamentals Fundamental Fundamenta Analysis