The minimax optimization over Riemannian manifolds (possibly nonconvex constraints) has
been actively applied to solve many problems, such as robust dimensionality reduction and …

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 min-max optimization problems on Riemannian manifolds. We
introduce a Riemannian Hamiltonian function, minimization of which serves as a proxy for …

Numerous applications in machine learning and data analytics can be formulated as
equilibrium computation over Riemannian manifolds. Despite the extensive investigation of …

In this paper, we consider Riemannian online convex optimization with dynamic regret. First,
we propose two novel algorithms, namely the Riemannian Online Optimistic Gradient …

Convex programming plays a fundamental role in machine learning, data science, and
engineering. Testing convexity structure in nonlinear programs relies on verifying the …

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 …

We propose a globally-accelerated, first-order method for the optimization of smooth and
(strongly or not) geodesically-convex functions in a wide class of Hadamard manifolds. We …

Bilevel optimization has seen an increasing presence in various domains of applications. In
this work, we propose a framework for solving bilevel optimization problems where variables …

Deciding whether saddle points exist or are approximable for nonconvex-nonconcave
problems is usually intractable. This paper takes a step towards understanding a broad …