Related papers: Nearest $\Omega$-stable matrix via Riemannian opti…

The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…

We consider the stability of Robust Optimization problems with respect to perturbations in their uncertainty sets. We focus on Linear Optimization problems, including those with a possibly infinite number of constraints, also known as…

This paper studies the problem of maximizing the sum of traces of matrix quadratic forms on a product of Stiefel manifolds. This orthogonal trace-sum maximization (OTSM) problem generalizes many interesting problems such as generalized…

Riemannian submanifold optimization with momentum is computationally challenging because, to ensure that the iterates remain on the submanifold, we often need to solve difficult differential equations. Here, we simplify such difficulties…

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…

This work aims to solve a stochastic nonconvex nonsmooth composite optimization problem. Previous works on composite optimization problem requires the major part to satisfy Lipschitz smoothness or some relaxed smoothness conditions, which…

We consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest…

In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our…

We investigate numerically efficient approximations of eigenspaces associated to symmetric and general matrices. The eigenspaces are factored into a fixed number of fundamental components that can be efficiently manipulated (we consider…

We describe the recursive algorithmic procedure to compute the stabilizers of the group of complex orthogonal matrices with respect to the action of similarity on the set of all symmetric matrices. Futhermore, lower bounds for dimensions of…

In many contexts one encounters Hermitian operators $M$ on a Hilbert space whose dimension is so large that it is impossible to write down all matrix entries in an orthonormal basis. How does one determine whether such $M$ is positive…

We examine a wide class of stochastic approximation algorithms for solving (stochastic) nonlinear problems on Riemannian manifolds. Such algorithms arise naturally in the study of Riemannian optimization, game theory and optimal transport,…

A method is given for solving an optimal H2 approximation problem for SISO linear time-invariant stable systems. The method, based on constructive algebra, guarantees that the global optimum is found; it does not involve any gradient-based…

Let $A$ be a square matrix with a given structure (e.g. real matrix, sparsity pattern, Toeplitz structure, etc.) and assume that it is unstable, i.e. at least one of its eigenvalues lies in the complex right half-plane. The problem of…

We characterize optimal rank-1 matrix approximations with Hankel or Toeplitz structure with regard to two different norms, the Frobenius norm and the spectral norm, in a new way. More precisely, we show that these rank-1 matrix…

In this paper we give an explicit solution to the rank constrained matrix approximation in Frobenius norm, which is a generalization of the classical approximation of an m by n matrix A by a matrix of rank k at most.

We study the stability of entropically regularized optimal transport with respect to the marginals. Lipschitz continuity of the value and H\"older continuity of the optimal coupling in $p$-Wasserstein distance are obtained under general…

Given an input matrix polynomial whose coefficients are floating point numbers, we consider the problem of finding the nearest matrix polynomial which has rank at most a specified value. This generalizes the problem of finding a nearest…

We study the convergence of the Riemannian steepest descent algorithm on the Grassmann manifold for minimizing the block version of the Rayleigh quotient of a symmetric matrix. Even though this problem is non-convex in the Euclidean sense…

We consider the matrix completion problem under a form of row/column weighted entrywise sampling, including the case of uniform entrywise sampling as a special case. We analyze the associated random observation operator, and prove that with…