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The problem of determining the configuration of points from partial distance information, known as the Euclidean Distance Geometry (EDG) problem, is fundamental to many tasks in the applied sciences. In this paper, we propose two algorithms…
The batch exponentiated gradient (EG) method provides a principled approach to convex smooth minimization on the probability simplex or the space of quantum density matrices. However, it is not always guaranteed to converge. Existing…
In this paper, we introduce an inertial version of the Proximal Incremental Aggregated Gradient method (PIAG) for minimizing the sum of smooth convex component functions and a possibly nonsmooth convex regularization function.…
Recently, minimax optimization received renewed focus due to modern applications in machine learning, robust optimization, and reinforcement learning. The scale of these applications naturally leads to the use of first-order methods.…
In this paper, we study the proximal incremental aggregated gradient(PIAG) algorithm for minimizing the sum of L-smooth nonconvex component functions and a proper closed convex function. By exploiting the L-smooth property and with the help…
A function is exponentially concave if its exponential is concave. We consider exponentially concave functions on the unit simplex. In a previous paper we showed that gradient maps of exponentially concave functions provide solutions to a…
We focus on the problem of minimizing the sum of smooth component functions (where the sum is strongly convex) and a non-smooth convex function, which arises in regularized empirical risk minimization in machine learning and distributed…
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…
We study optimization over Riemannian embedded submanifolds, where the objective function is relatively smooth in the ambient Euclidean space. Such problems have broad applications but are still largely unexplored. We introduce two…
Despite the established convergence theory of Optimistic Gradient Descent Ascent (OGDA) and Extragradient (EG) methods for the convex-concave minimax problems, little is known about the theoretical guarantees of these methods in nonconvex…
Elliptically-contoured distributions (ECD) play a significant role, in computer vision, image processing, radar, and biomedical signal processing. Maximum likelihood. estimation (MLE) of ECD leads to a system of non-linear equations,…
Gradient descent methods are fundamental first-order optimization algorithms in both Euclidean spaces and Riemannian manifolds. However, the exact gradient is not readily available in many scenarios. This paper proposes a novel inexact…
Information geometry applies concepts in differential geometry to probability and statistics and is especially useful for parameter estimation in exponential families where parameters are known to lie on a Riemannian manifold. Connections…
Convex optimization over the spectrahedron, i.e., the set of all real $n\times n$ positive semidefinite matrices with unit trace, has important applications in machine learning, signal processing and statistics, mainly as a convex…
A celebrated method for Variational Inequalities (VIs) is Extragradient (EG), which can be viewed as a standard discrete-time integration scheme. With this view in mind, in this paper we show that EG may suffer from discretization bias when…
Riemannian convex optimization and minimax optimization have recently drawn considerable attention. Their appeal lies in their capacity to adeptly manage the non-convexity of the objective function as well as constraints inherent in the…
Equilibrium computation on Riemannian manifolds provides a unifying framework for numerous problems in machine learning and data analytics. One of the simplest yet most fundamental methods is Riemannian gradient descent (RGD). While its…
We present a subgradient method for minimizing non-smooth, non-Lipschitz convex optimization problems. The only structure assumed is that a strictly feasible point is known. We extend the work of Renegar [5] by taking a different…
Orthogonal Gradient Descent (OGD) has emerged as a powerful method for continual learning. However, its Euclidean projections do not leverage the underlying information-geometric structure of the problem, which can lead to suboptimal…
Classical assumptions like strong convexity and Lipschitz smoothness often fail to capture the nature of deep learning optimization problems, which are typically non-convex and non-smooth, making traditional analyses less applicable. This…