In this work, we consider monotone Riemannian Variational Inequality Problems (RVIPs),
which encompass both Riemannian convex optimization and minimax optimization as …

In this paper we study two-player bilinear zero-sum games with constrained strategy spaces.
An instance of natural occurrences of such constraints is when mixed strategies are used …

Explicit, momentum-based dynamics for optimizing functions defined on Lie groups was
recently constructed, based on techniques such as variational optimization and left …

The problem of optimization on Stiefel manifold, ie, minimizing functions of (not necessarily
square) matrices that satisfy orthogonality constraints, has been extensively studied. Yet, a …

This article considers the generative modeling of the states of quantum systems, and an
approach based on denoising diffusion model is proposed. The key contribution is an …

In this letter, we propose a bio-inspired derivative-free optimization algorithm capable of
minimizing objective functions with vanishing or exploding gradients. The proposed method …

This article suggests that deterministic Gradient Descent, which does not use any stochastic
gradient approximation, can still exhibit stochastic behaviors. In particular, it shows that if the …

It is well known that symplectic integrators lose their near energy preservation properties
when variable time-steps are used. The most common approach to combining adaptive time …

The recent interest in structure preserving stochastic Lagrangian and Hamiltonian systems
raises questions regarding how such models are to be understood and the principles …

Geometric numerical integration has recently been exploited to design symplectic
accelerated optimization algorithms by simulating the Bregman Lagrangian and Hamiltonian …