A subgradient duality theorem

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.

Duality Theorem for Motives

A general duality theorem for the category of motives is established, with a short, simple, and self-contained proof. Introduction Recently, due to the active study of cohomological invariants in algebraic geometry, “transplantation” of classical topological constructions to the algebraic-geometrical “soil” seems to be rather important. In particular, it is very interesting to study topological...

On a Duality Theorem of Wakamatsu

Let R be a left coherent ring, S a right coherent ring and RU a generalized tilting module, with S = End(RU ) satisfying the condition that each finitely presented left R-module X with ExtR(X,U )= 0 for any i ≥ 1 is U -torsionless. If M is a finitely presented left R-module such that ExtR(M,U )= 0 for any i ≥ 0 with i 6= n (where n is a nonnegative integer), then ExtS(Ext n R(M,U ),U ) ∼= M and...