Related papers: Newton's method on Gra{\ss}mann manifolds

This paper is devoted to studying the global and finite convergence of the semi-smooth Newton method for solving a piecewise linear system that arises in cone-constrained quadratic programming problems and absolute value equations. We first…

An algorithm for the computation of global discrete conformal parametrizations with prescribed global holonomy signatures for triangle meshes was recently described in [Campen and Zorin 2017]. In this paper we provide a detailed analysis of…

Unconstrained convex optimization problems have enormous applications in various field of science and engineering. Different iterative methods are available in literature to solve such problem, and Newton method is among the oldest and…

Machine learning algorithms, both in their classical and quantum versions, heavily rely on optimization algorithms based on gradients, such as gradient descent and alike. The overall performance is dependent on the appearance of local…

Retraction-free approaches offer attractive low-cost alternatives to Riemannian methods on the Stiefel manifold, but they are often first-order, which may limit the efficiency under high-accuracy requirements. To this end, we propose a…

This paper proposes a Newton-type method to solve numerically the eigenproblem of several diagonalizable matrices, which pairwise commute. A classical result states that these matrices are simultaneously diagonalizable. From a suitable…

We consider Riemannian optimization problems with inequality and equality constraints and analyze a class of Riemannian interior point methods for solving them. The algorithm of interest consists of outer and inner iterations. We show that,…

We study the problem of minimizing a sum of convex objective functions where the components of the objective are available at different nodes of a network and nodes are allowed to only communicate with their neighbors. The use of…

Projected gradient descent and its Riemannian variant belong to a typical class of methods for low-rank matrix estimation. This paper proposes a new Nesterov's Accelerated Riemannian Gradient algorithm by efficient orthographic retraction…

In the paper, a variant of the \ssstar Newton method is developed for the numerical solution of generalized equations, in which the multi-valued part is a so-called SCD (subspace containing derivative) mapping. Under a rather mild…

In this paper, we propose a distributed algorithm for solving large-scale separable convex problems using Lagrangian dual decomposition and the interior-point framework. By adding self-concordant barrier terms to the ordinary Lagrangian, we…

Gradient-based (a.k.a. `first order') optimization algorithms are routinely used to solve large scale non-convex problems. Yet, it is generally hard to predict their effectiveness. In order to gain insight into this question, we revisit the…

In this paper, we define the geometric median of a probability measure on a Riemannian manifold, give its characterization and a natural condition to ensure its uniqueness. In order to calculate the median in practical cases, we also…

This is a documentation of a framework for robot motion optimization that aims to draw on classical constrained optimization methods. With one exception the underlying algorithms are classical ones: Gauss-Newton (with adaptive step size and…

We present a proximal augmented Lagrangian based solver for general convex quadratic programs (QPs), relying on semismooth Newton iterations with exact line search to solve the inner subproblems. The exact line search reduces in this case…

In this paper, we derive new model formulations for computing generalized singular values of a Grassman matrix pair. These new formulations make use of truncated filter matrices to locate the $i$-th generalized singular value of a Grassman…

This paper studies large-scale optimization problems on Riemannian manifolds whose objective function is a finite sum of negative log-probability losses. Such problems arise in various machine learning and signal processing applications. By…

Graph Neural Networks (GNNs) are a powerful representational tool for solving problems on graph-structured inputs. In almost all cases so far, however, they have been applied to directly recovering a final solution from raw inputs, without…

We develop a theory of arithmetic Newton polygons of higher order, that provides the factorization of a separable polynomial over a $p$-adic field, together with relevant arithmetic information about the fields generated by the irreducible…

We use differential equations based approaches to provide some {\it \textbf{physics}} insights into analyzing the dynamics of popular optimization algorithms in machine learning. In particular, we study gradient descent, proximal gradient…