Related papers: A Riemannian trust-region method for low-rank tens…
We propose a new algorithm to solve optimization problems of the form $\min f(X)$ for a smooth function $f$ under the constraints that $X$ is positive semidefinite and the diagonal blocks of $X$ are small identity matrices. Such problems…
Robust low-rank matrix completion (RMC), or robust principal component analysis with partially observed data, has been studied extensively for computer vision, signal processing and machine learning applications. This problem aims to…
In this paper, we show that the low rank matrix completion problem can be reduced to the problem of finding the rank of a certain tensor.
We introduce a two-level trust-region method (TLTR) for solving unconstrained nonlinear optimization problems. Our method uses a composite iteration step, which is based on two distinct search directions. The first search direction is…
We propose an extremely versatile approach to address a large family of matrix nearness problems, possibly with additional linear constraints. Our method is based on splitting a matrix nearness problem into two nested optimization problems,…
Low rank matrix and tensor completion problems are to recover the incomplete two and higher order data by using their low rank structures. The essential problem in the matrix and tensor completion problems is how to improve the efficiency.…
Optimization on Riemannian manifolds widely arises in eigenvalue computation, density functional theory, Bose-Einstein condensates, low rank nearest correlation, image registration, and signal processing, etc. We propose an adaptive…
The problem of recovering the configuration of points from their partial pairwise distances, referred to as the Euclidean Distance Matrix Completion (EDMC) problem, arises in a broad range of applications, including sensor network…
The low-rank matrix completion problem can be succinctly stated as follows: given a subset of the entries of a matrix, find a low-rank matrix consistent with the observations. While several low-complexity algorithms for matrix completion…
A Riemannian gradient descent algorithm and a truncated variant are presented to solve systems of phaseless equations $|Ax|^2=y$. The algorithms are developed by exploiting the inherent low rank structure of the problem based on the…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
We consider trust-region methods for solving optimization problems where the objective is the sum of a smooth, nonconvex function and a nonsmooth, convex regularizer. We extend the global convergence theory of such methods to include…
Conjugate gradient (CG) methods are widely acknowledged as efficient for minimizing continuously differentiable functions in Euclidean spaces. In recent years, various CG methods have been extended to Riemannian manifold optimization, but…
In this paper, we study Riemannian zeroth-order optimization in settings where the underlying Riemannian metric $g$ is geodesically incomplete, and the goal is to approximate stationary points with respect to this incomplete metric. To…
Radio maps are important enablers for many applications in wireless networks, ranging from network planning and optimization to fingerprint based localization. Sampling the complete map is prohibitively expensive in practice, so methods for…
In this paper, we propose a general procedure for establishing the geometric landscape connections of a Riemannian optimization problem under the embedded and quotient geometries. By applying the general procedure to the fixed-rank positive…
Gradient descent with momentum has been widely applied in various signal processing and machine learning tasks, demonstrating a notable empirical advantage over standard gradient descent. However, momentum-based distributed Riemannian…
From optimal transport to robust dimensionality reduction, a plethora of machine learning applications can be cast into the min-max optimization problems over Riemannian manifolds. Though many min-max algorithms have been analyzed in the…
The completion of tensors, or high-order arrays, attracts significant attention in recent research. Current literature on tensor completion primarily focuses on recovery from a set of uniformly randomly measured entries, and the required…
Motivated by the problem of learning a linear regression model whose parameter is a large fixed-rank non-symmetric matrix, we consider the optimization of a smooth cost function defined on the set of fixed-rank matrices. We adopt the…