Publication

Stochastic Three-Composite Convex Minimization with a Linear Operator

Volkan Cevher
2018
Conference Papers

Abstract

We develop a primal-dual convex minimization framework to solve a class of stochastic convex three-composite problem with a linear operator. We consider the cases where the problem is both convex and strongly convex and analyze the convergence of the proposed algorithm in both cases. In addition, we extend the proposed framework to deal with additional constraint sets and multiple non-smooth terms. We provide numerical evidence on graph-guided sparse logistic regression, fused lasso and overlapped group lasso, to demonstrate the superiority of our approach to the state-of-the-art.

Official source

https://infoscience.epfl.ch/entities/publication/1383cd23-d01c-4c7a-80b7-18517255d580

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Volkan Cevher
2018
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/1383cd23-d01c-4c7a-80b7-18517255d580

About this result

Related concepts (32)

Convex function

In mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above the graph between the two points. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set. A twice-differentiable function of a single variable is convex if and only if its second derivative is nonnegative on its entire domain.

Bounded operator

In functional analysis and operator theory, a bounded linear operator is a linear transformation between topological vector spaces (TVSs) and that maps bounded subsets of to bounded subsets of If and are normed vector spaces (a special type of TVS), then is bounded if and only if there exists some such that for all The smallest such is called the operator norm of and denoted by A bounded operator between normed spaces is continuous and vice versa. The concept of a bounded linear operator has been extended from normed spaces to all topological vector spaces.

Continuous linear operator

In functional analysis and related areas of mathematics, a continuous linear operator or continuous linear mapping is a continuous linear transformation between topological vector spaces. An operator between two normed spaces is a bounded linear operator if and only if it is a continuous linear operator. Continuous function (topology) and Discontinuous linear map Bounded operator Suppose that is a linear operator between two topological vector spaces (TVSs). The following are equivalent: is continuous.

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