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Geometric medians on product manifolds are sensitive to the relative scaling of factor metrics because the median objective couples the factors rather than separating them. We study this scale-selection problem and first prove that naive…

The high-index saddle dynamics (HiSD) method provides a powerful framework for finding saddle points and constructing solution landscapes. While originally derived for nondegenerate critical points, HiSD has demonstrated empirical success…

In this note we take a new look at the local convergence of alternating optimization methods for low-rank matrices and tensors. Our abstract interpretation as sequential optimization on moving subspaces yields insightful reformulations of…

Stochastic optimisation problems minimise expectations of random cost functions. We use 'optimise then discretise' method to solve stochastic optimisation. In our approach, accurate quadrature methods are required to calculate the…

This paper focuses on minimizing a smooth function combined with a nonsmooth regularization term on a compact Riemannian submanifold embedded in the Euclidean space under a decentralized setting. Typically, there are two types of approaches…

We introduce a novel family of invariant, convex, and non-quadratic functionals that we employ to derive regularized solutions of ill-posed linear inverse imaging problems. The proposed regularizers involve the Schatten norms of the Hessian…

We consider stochastic optimization problems which use observed data to estimate essential characteristics of the random quantities involved. Sample average approximation (SAA) or empirical (plug-in) estimation are very popular ways to use…

The truncated singular value decomposition (SVD) of the measurement matrix is the optimal solution to the_representation_ problem of how to best approximate a noisy measurement matrix using a low-rank matrix. Here, we consider the…

We develop a numerical methodology for the computation of entanglement measures for mixed quantum states. Using the well-known Schr\"odinger-HJW theorem, the computation of convex roof entanglement measures is reframed as a search for…

In this paper we study the extraction of representative elements in the data stream model in the form of submodular maximization. Different from the previous work on streaming submodular maximization, we are interested only in the recent…

Neural signed distance functions (SDFs) have become a powerful representation for geometric reconstruction from point clouds, yet they often require both gradient- and curvature-based regularization to suppress spurious warp and preserve…

In this paper, we present a new stochastic algorithm, namely the stochastic block mirror descent (SBMD) method for solving large-scale nonsmooth and stochastic optimization problems. The basic idea of this algorithm is to incorporate the…

Support vector machine (SVM) has attracted great attentions for the last two decades due to its extensive applications, and thus numerous optimization models have been proposed. To distinguish all of them, in this paper, we introduce a new…

Unconstrained optimization problems become more common in scientific computing and engineering applications with the rapid development of artificial intelligence, and numerical methods for solving them more quickly and efficiently have been…

Accurate robot odometry is essential for autonomous navigation. While numerous techniques have been developed based on various sensor suites, odometry estimation using only radar and IMU remains an underexplored area. Radar proves…

We analyse an iterative algorithm to minimize quadratic functions whose Hessian matrix $H$ is the expectation of a random symmetric $d\times d$ matrix. The algorithm is a variant of the stochastic variance reduced gradient (SVRG). In…

We present an algorithm for minimizing a sum of functions that combines the computational efficiency of stochastic gradient descent (SGD) with the second order curvature information leveraged by quasi-Newton methods. We unify these…

We consider several classes of highly important semidefinite optimization problems that involve both a convex objective function (smooth or nonsmooth) and additional linear or nonlinear smooth and convex constraints, which are ubiquitous in…

Sliced Optimal Transport (OT) simplifies the OT problem in high-dimensional spaces by projecting supports of input measures onto one-dimensional lines and then exploiting the closed-form expression of the univariate OT to reduce the…

We consider factoring low-rank tensors in the presence of outlying slabs. This problem is important in practice, because data collected in many real-world applications, such as speech, fluorescence, and some social network data, fit this…