Mikhail A. Bragin • Peter B. Luh • Joseph H. Yan • Nanpeng Yu • Gary A. Stern Communicated by Fabián Flores-Bazàn Abstract Studies have shown that the surrogate subgradient method, to optimize non-smooth dual functions within the Lagrangian relaxation framework, can lead to significant computational improvements as compared to the subgradient method. The key idea is to obtain surrogate subgradi...

A study of the convergence properties of spectral projected subgradient method is presented and the convergence is shown. The convergence is based on spectral projected gradient approach. Some updates of the spectral projected subgradient are described.

Time series averaging in dynamic time warping (DTW) spaces has been successfully applied to improve pattern recognition systems. This article proposes and analyzes subgradient methods for the problem of finding a sample mean in DTW spaces. The class of subgradient methods generalizes existing sample mean algorithms such as DTW Barycenter Averaging (DBA). We show that DBA is a majorize-minimize ...

In the recent paper [3], it was shown that the stochastic subgradient method applied to a weakly convex problem, drives the gradient of the Moreau envelope to zero at the rate O(k−1/4). In this supplementary note, we present a stochastic subgradient method for minimizing a convex function, with the improved rate Õ(k−1/2).

In this paper, we introduce a stochastic projected subgradient method for weakly convex (i.e., uniformly prox-regular) nonsmooth, nonconvex functions—a wide class of functions which includes the additive and convex composite classes. At a high-level, the method is an inexact proximal point iteration in which the strongly convex proximal subproblems are quickly solved with a specialized stochast...

The minimization of nonlinearly constrained network flow problems can be performed by using approximate subgradient methods. The idea is to solve this kind of problem by means of primal-dual methods, given that the minimization of nonlinear network flow problems can be efficiently done by exploiting the network structure. In this work it is proposed to solve the dual problem by using 2subgradie...

Abstract For the purpose of this article, we introduce a modified form generalized system variational inclusions, called inclusion problems (GSMVIP). This problem reduces to classical and inequalities problems. Motivated by several recent results related subgradient extragradient method, propose new method for finding common element set solutions GSMVIP finite family Under suitable assumptions,...

Subgradient methods are popular tools for nonsmooth, convex minimization , especially in the context of Lagrangean relaxation; their simplicity has been a main contribution to their success. As a consequence of the nonsmoothness, it is not straightforward to monitor the progress of a subgradient method in terms of the approximate fulllment of optimality conditions, since the subgradients used i...