More on subgradient duality

Subgradient Optimization, Generalized Programming, and Nonconvex Duality

Duality between subgradient and conditional gradient methods

Given a convex optimization problem and its dual, there are many possible firstorder algorithms. In this paper, we show the equivalence between mirror descent algorithms and algorithms generalizing the conditional gradient method. This is done through convex duality and implies notably that for certain problems, such as for supervised machine learning problems with nonsmooth losses or problems ...

rcss: Subgradient and duality approach for dynamic programming

This short paper gives an introduction to the \emph{rcss} package. The R package \emph{rcss} provides users with a tool to approximate the value functions in the Bellman recursion using convex piecewise linear functions formed using operations on tangents. A pathwise method is then used to gauge the quality of the numerical results.

On Subgradient Projectors

The subgradient projector is of considerable importance in convex optimization because it plays the key role in Polyak’s seminal work — and the many papers it spawned — on subgradient projection algorithms for solving convex feasibility problems. In this paper, we offer a systematic study of the subgradient projector. Fundamental properties such as continuity, nonexpansiveness, and monotonicity...

On a new G-frame and duality

We introduce a new g-frame (singleton g-frame), g-orthonormal basis and g-Riesz basis and study corresponding notions in some other generalizations of frames.Also, we investigate duality  for some kinds of g-frames. Finally, we illustrate an example which provides a  suitable translation from discrete frames to Sun's g-frames.