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We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the…
This paper addresses the global optimization of the sum of the Rayleigh quotient and the generalized Rayleigh quotient on the unit sphere. While various methods have been proposed for this problem, they fail to reliably converge to the…
The approximation of tensors is important for the efficient numerical treatment of high dimensional problems, but it remains an extremely challenging task. One of the most popular approach to tensor approximation is the alternating least…
We propose an iterative algorithm for low-rank matrix completion that can be interpreted as an iteratively reweighted least squares (IRLS) algorithm, a saddle-escaping smoothing Newton method or a variable metric proximal gradient method…
We present a non-conforming least squares method for approximating solutions of second order elliptic problems with discontinuous coefficients. The method is based on a general Saddle Point Least Squares (SPLS) method introduced in previous…
The resolution and calibration of pure spectra of minority components in measurements of chemical mixtures without prior knowledge of the mixture is a challenging problem. In this work, a combination of band target entropy minimization…
We present a two-stage least-squares method to inverse medium problems of reconstructing multiple unknown coefficients simultaneously from noisy data. A direct sampling method is applied to detect the location of the inhomogeneity in the…
We present a hierarchy of tractable relaxations to obtain lower bounds on the minimum value of a polynomial over a constraint set defined by polynomial equations. In contrast to previous convex relaxation techniques for this problem, our…
Bearing-only Target Motion Analysis (TMA) is a promising technique for passive tracking in various applications as a bearing angle is easy to measure. Despite its advantages, bearing-only TMA is challenging due to the nonlinearity of the…
The article concerns compressed sensing methods in the quaternion algebra. We prove that it is possible to uniquely reconstruct - by $\ell_1$ norm minimization - a sparse quaternion signal from a limited number of its real linear…
This study presents a generalised least squares based method for fitting polygons and ellipses to data points. The method is based on a trigonometric fitness function that approximates a unit shape accurately, making it applicable to…
In this paper we present new algorithms and analysis for the linear inverse sensor placement and scheduling problems over multiple time instances with power and communications constraints. The proposed algorithms, which deal directly with…
A Bayesian approach termed BAyesian Least Squares Optimization with Nonnegative L1-norm constraint (BALSON) is proposed. The error distribution of data fitting is described by Gaussian likelihood. The parameter distribution is assumed to be…
Quantization of signals is an integral part of modern signal processing applications, such as sensing, communication, and inference. While signal quantization provides many physical advantages, it usually degrades the subsequent estimation…
Due to the insufficient measurements in the distribution system state estimation (DSSE), full observability and redundant measurements are difficult to achieve without using the pseudo measurements. The matrix completion state estimation…
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…
In this paper, based on the theory of adjoint operators and dual norms, we define condition numbers for a linear solution function of the weighted linear least squares problem. The explicit expressions of the normwise and componentwise…
In this paper, we account for approaches of sparse recovery from large underdetermined linear models with perturbation present in both the measurements and the dictionary matrix. Existing methods have high computation and low efficiency.…
We introduce the implicitly constrained least squares (ICLS) classifier, a novel semi-supervised version of the least squares classifier. This classifier minimizes the squared loss on the labeled data among the set of parameters implied by…
Robust regression techniques rely on least-squares optimization, which works well for Gaussian noise but fails in the presence of asymmetric structured noise. We propose a hybrid neural-symbolic architecture where a transformer encoder…