Related papers: Understanding Riemannian Acceleration via a Proxim…

Moving Horizon Estimation~(MHE) is essentially an optimization-based approach designed to estimate the states of dynamic systems within a moving time horizon. Traditional MHE solutions become computationally prohibitive due to the…

The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable…

We study the connections between ordinary differential equations and optimization algorithms in a non-Euclidean setting. We propose a novel accelerated algorithm for minimising convex functions over a convex constrained set. This algorithm…

Based on SGD, previous works have proposed many algorithms that have improved convergence speed and generalization in stochastic optimization, such as SGDm, AdaGrad, Adam, etc. However, their convergence analysis under non-convex conditions…

This paper proposes an original Riemmanian geometry for low-rank structured elliptical models, i.e., when samples are elliptically distributed with a covariance matrix that has a low-rank plus identity structure. The considered geometry is…

Riemannian manifolds have been widely employed for video representations in visual classification tasks including video-based face recognition. The success mainly derives from learning a discriminant Riemannian metric which encodes the…

We propose a novel Riemannian method for solving the Extreme multi-label classification problem that exploits the geometric structure of the sparse low-dimensional local embedding models. A constrained optimization problem is formulated as…

In this paper, we aim to accelerate a preconditioned alternating direction method of multipliers (pADMM), whose proximal terms are convex quadratic functions, for solving linearly constrained convex optimization problems. To achieve this,…

We consider the recently introduced notion of denominators of Pad\'e--like approximation problems on a Riemann surface. These denominators are related as in the classical case to the notion of orthogonality over a contour. We investigate a…

In this paper, we introduce the notion of generalized $\epsilon$-stationarity for a class of nonconvex and nonsmooth composite minimization problems on compact Riemannian submanifold embedded in Euclidean space. To find a generalized…

Recent advances in convex optimization have leveraged computer-assisted proofs to develop optimized first-order methods that improve over classical algorithms. However, each optimized method is specially tailored for a particular problem…

We present a unifying framework for adapting the update direction in gradient-based iterative optimization methods. As natural special cases we re-derive classical momentum and Nesterov's accelerated gradient method, lending a new intuitive…

We study optimization problems on Hadamard manifolds, motivated by recent advances in geometric approaches to optimization on curved spaces, particularly those involving the structure of Busemann functions. We introduce a projection based…

We investigate the problem of minimizing Kullback-Leibler divergence between a linear model $Ax$ and a positive vector $b$ in different convex domains (positive orthant, $n$-dimensional box, probability simplex). Our focus is on the SMART…

Graph data often exhibits complex geometric heterogeneity, where structures with varying local curvature, such as tree-like hierarchies and dense communities, coexist within a single network. Existing geometric GNNs, which embed graphs into…

Approximate graph pattern mining (A-GPM) is an important data analysis tool for many graph-based applications. There exist sampling-based A-GPM systems to provide automation and generalization over a wide variety of use cases. However,…

This work proposes a unifying probabilistic framework for the design of robustly asymptotically stable moving-horizon estimators (MHE) for discrete-time nonlinear systems, and a mechanism to incorporate differential privacy in…

Shape optimization based on the shape calculus is numerically mostly performed by means of steepest descent methods. This paper provides a novel framework to analyze shape-Newton optimization methods by exploiting a Riemannian perspective.…

In this paper, we introduce a Gaussian process based moving horizon estimation (MHE) framework. The scheme is based on offline collected data and offline hyperparameter optimization. In particular, compared to standard MHE schemes, we…

Symmetric Positive Definite (SPD) matrices have received wide attention in machine learning due to their intrinsic capacity to encode underlying structural correlation in data. Many successful Riemannian metrics have been proposed to…