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Erschienen in:
2015 | OriginalPaper | Buchkapitel
6. Keynote Iterative Methods
verfasst von : Juan Peypouquet
Erschienen in: Convex Optimization in Normed Spaces
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Abstract
In this chapter we give an introduction to the basic (sub)gradient-based methods for minimizing a convex function on a Hilbert space. We pay special attention to the proximal point algorithm and the gradient method, which are interpreted as time discretizations of the steepest descent differential inclusion. Moreover, these methods, along with some extensions and variants, are the building blocks for other - more sophisticated - methods that exploit particular features of the problems, such as the structure of the feasible (or constraint) set. The choice of proximal- or gradient-type schemes depends strongly on the regularity of the objective function.
Throughout this chapter, H is a real Hilbert space.