BibTeX
@MISC{Rockafellar70convexanalysis,
author = {R. Tyrrell Rockafellar},
title = {Convex Analysis},
year = {1970}
}
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Abstract
In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a long time, ‘variational ’ problems have been identified mostly with the ‘calculus of variations’. In that venerable subject, built around the minimization of integral functionals, constraints were relatively simple and much of the focus was on infinite-dimensional function spaces. A major theme was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory progressed also to the study of so-called stationary points, critical points, and other indications of singularity that a point might have relative to its neighbors, especially in association with existence theorems for differential equations.
Keyphrases
convex analysis long time variational theory title variational analysis venerable subject infinite-dimensional function space critical point existence theorem major theme differential equation nonlinear system integral functionals broad spectrum unified framework variational principle so-called stationary point mathematical theory variational problem
