Abstract Extragradient method (EG)(Korpelevich, 1976) is one of the most popular methods
for solving saddle point and variational inequalities problems (VIP). Despite its long history …

Motivated by structures that appear in deep neural networks, we investigate nonlinear
composite models alternating proximity and affine operators defined on different spaces. We …

We propose a methodology for studying the performance of common splitting methods
through semidefinite programming. We prove tightness of the methodology and demonstrate …

Algorithms for min-max optimization and variational inequalities are often studied under
monotonicity assumptions. Motivated by non-monotone machine learning applications, we …

We consider the monotone inclusion problem with a sum of 3 operators, in which 2 are
monotone and 1 is monotone-Lipschitz. The classical Douglas–Rachford and forward …

Scaled graphs allow for graphical analysis of nonlinear systems, but are generally difficult to
compute. The aim of this paper is to develop a method for approximating the scaled graph of …

Since Nesterov's seminal 1983 work, many accelerated first-order optimization methods
have been proposed, but their analyses lacks a common unifying structure. In this work, we …

Traditional Federated Learning (FL) approaches assume collaborative clients with aligned
objectives working towards a shared global model. However, in many real-world scenarios …

Maximal monotonicity is explored as a generalization of the linear theory of passivity, aiming
at an algorithmic input/output analysis of physical models. The theory is developed for …

We use the recently introduced concept of a scaled relative graph (SRG) to develop a
graphical analysis of input–output properties of feedback systems. The SRG of a nonlinear …