In this work, we propose a simple modification of the forward-backward splitting method for
finding a zero in the sum of two monotone operators. Our method converges under the same …

In this work, we study the computational complexity of reducing the squared gradient
magnitude for smooth minimax optimization problems. First, we present algorithms with …

Convergent sequences of real numbers play a fundamental role in many different problems
in system theory, eg, in Lyapunov stability analysis, as well as in optimization theory and …

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

We investigate a structured class of nonconvex-nonconcave min-max problems exhibiting
so-called\emph {weak Minty} solutions, a notion which was only recently introduced, but is …

In the framework of real Hilbert spaces, we study continuous in time dynamics as well as
numerical algorithms for the problem of approaching the set of zeros of a single-valued …

We improve the understanding of the golden ratio algorithm, which solves monotone
variational inequalities (VI) and convex-concave min-max problems via the distinctive …

The introduction of the Hessian damping in the continuous version of Nesterov's accelerated
gradient method provides, by temporal discretization, fast proximal gradient algorithms …

Motivated by the training of generative adversarial networks (GANs), we study methods for
solving minimax problems with additional nonsmooth regularizers. We do so by employing …

Several new accelerated methods in minimax optimization and fixed-point iterations have
recently been discovered, and, interestingly, they rely on a mechanism distinct from …