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We study preconditioned gradient-based optimization methods where the preconditioning matrix has block-diagonal form. Such a structural constraint comes with the advantage that the update computation is block-separable and can be…
This paper introduces inexact versions of several block-splitting preconditioners for solving the three-by-three block linear systems arising from a special class of indefinite least squares problems. We first establish the convergence…
Matrix completion is a problem that arises in many data-analysis settings where the input consists of a partially-observed matrix (e.g., recommender systems, traffic matrix analysis etc.). Classical approaches to matrix completion assume…
In this work, we revisit nonlinear generalized minimal residual method (NGMRES) applied to nonlinear problems. NGMRES is used to accelerate the convergence of fixed-point iterations, which can substantially improve the performance of the…
We consider the problem of metric learning subject to a set of constraints on relative-distance comparisons between the data items. Such constraints are meant to reflect side-information that is not expressed directly in the feature vectors…
The linear model, in which a set of observations is assumed to be given by a linear combination of columns of a matrix, has long been the mainstay of the statistics and signal processing literature. One particular challenge for inference…
We address the solution of the distributed control problem for the steady, incompressible Navier--Stokes equations. We propose an inexact Newton linearization of the optimality conditions. Upon discretization by a finite element scheme, we…
We consider minimax (saddle-point) problems of the form max_{c \in C} min_{\beta \in S} g(c; \beta), where C and S are compact convex sets, and g is concave-convex. Applying the Alternating Direction Method of Multipliers (ADMM) requires…
The conjugate gradient method (CG) has long been the workhorse for inner-iterations of second-order algorithms for large-scale nonconvex optimization. Prominent examples include line-search based algorithms, e.g., Newton-CG, and those based…
For some typical and widely used non-convex half-quadratic regularization models and the Ambrosio-Tortorelli approximate Mumford-Shah model, based on the Kurdyka-\L ojasiewicz analysis and the recent nonconvex proximal algorithms, we…
A method for locating first order saddle points on the energy surface of a magnetic system is described and several applications presented where the mechanism of various magnetic transitions is identified. The starting point for the…
In the literature, there exist several studies on symbol-based multigrid methods for the solution of linear systems having structured coefficient matrices. In particular, the convergence analysis for such methods has been obtained in an…
Many modern applications require detecting change points in complex sequential data. Most existing methods for change point detection are unsupervised and, as a consequence, lack any information regarding what kind of changes we want to…
For the singular saddle-point problems with nonsymmetric positive definite $(1,1)$ block, we present a general constraint preconditioning (GCP) iteration method based on a singular constraint preconditioner. Using the properties of the…
We propose an alternating subgradient method with non-constant step sizes for solving convex-concave saddle-point problems associated with general convex-concave functions. We assume that the sequence of our step sizes is not summable but…
In this work, we propose new variants of Anderson acceleration and nonlinear GMRES for general fixed-point iterations, based on modified least-squares problems associated with the methods. To solve the underlying linear systems, we apply…
This paper deals with the state estimation for max-plus linear systems. This estimation is carried out following the ideas of the observer method for classical linear systems. The system matrices are assumed to be known, and the observation…
In this work, we describe how to construct matrices and block right-hand sides that exhibit a specified restarted block \gmres convergence pattern, such that the eigenvalues and Ritz values at each iteration can be chosen independent of the…
Kernel-based learning algorithms are widely used in machine learning for problems that make use of the similarity between object pairs. Such algorithms first embed all data points into an alternative space, where the inner product between…
The vast majority of evaluation metrics for machine translation are supervised, i.e., (i) are trained on human scores, (ii) assume the existence of reference translations, or (iii) leverage parallel data. This hinders their applicability to…