7 problems

Gradient-descent iteration conjecture. Gradient descent with the 5-factor retraction on $\mathrm{U}(N)$ should reach a point whose gradient norm is at most $\varepsilon$ in

Let the Riemannian optimization method proposed in this paper and the Das–Bora algorithm be applied to matrix pencils of increasing size, and compare their running times and the qu…

Let ${\cal M}$ be a complete Riemannian manifold with dimension $n\geq 2$, and let $p\in\Omega$ be a feasible point at which CRSC or RCPLD is satisfied. Here, $\Omega$ denotes the…

Let $f$ be a geodesically $ell$-smooth and geodesically strongly-convex-strongly-concave function on the geodesic metric spaces under consideration, and let Riemannian corrected ex…

Let mappings in the tangent space of a Riemannian manifold be used to simplify vector transports and related computations in numerical optimization. Efficiency conjecture. Such map…

Let the projection robust Wasserstein (PRW) distance and its convex relaxation, the sliced robust Wasserstein (SRW) distance, be computed for the same pair of probability measures.…

Real minimizer conjecture. The problem has a real solution $B\in\mathbb{R}^{n\times n}$. The conjecture concerns whether minimizing over all complex matrices can always be achieved…