Titlebook: Convex Optimization in Normed Spaces; Theory, Methods and Juan Peypouquet Book 2015 The Author(s) 2015 Convex optimization.nonlinear progr

fodlder

Convex Analysis and Subdifferential Calculus,ic (yet subtle) calculus rules, along with their remarkable consequences. Other important theoretical and practical tools, such as the Fenchel conjugate and the Lagrange multipliers, will also be studied. These are particularly useful for solving constrained problems.

尖叫

摇曳

失眠症

Problem-Solving Strategies,ures, and discuss some abstract tools for proving their convergence. Finally, we comment some ideas that are useful to simplify or reduce the problems, in order to make them tractable or more efficiently solved.

Charitable

Keynote Iterative Methods,oit 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.

树木中

2190-8354 , 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.978-3-319-13709-4978-3-319-13710-0Series ISSN 2190-8354 Series E-ISSN 2191-575X

Infant

Basic Functional Analysis, that will be needed throughout this book. A first section is devoted to general normed spaces. We begin by establishing some of their main properties, with an emphasis on the linear functions between spaces. This leads us to bounded linear functionals and the topological dual. Second, we review the

Apogee

Armada

Convex Analysis and Subdifferential Calculus,ion of their minimizers, on the other. We shall explore sufficient conditions for a convex function to be continuous, as well as several connections between convexity and differentiability. Next, we present the notion of subgradient, a generalization of the concept of derivative for nondifferentiabl

Ruptured-Disk

Examples,n the other, to provide useful characterizations allowing to determine them. In this chapter, we present a short selection of problems to illustrate some of those tools. We begin by revisiting some results from functional analysis concerning the maximization of bounded linear functionals and the rea