Related papers: An efficient algorithm for the minimal least squar…
We propose a solution strategy for linear systems arising in interior method optimization, which is suitable for implementation on hardware accelerators such as graphical processing units (GPUs). The current gold standard for solving these…
A sequential quadratic optimization algorithm is proposed for solving smooth nonlinear equality constrained optimization problems in which the objective function is defined by an expectation of a stochastic function. The algorithmic…
In this work, we consider two types of large-scale quadratic matrix equations: Continuous-time algebraic Riccati equations, which play a central role in optimal and robust control, and unilateral quadratic matrix equations, which arise from…
We present an accelerated, or 'look-ahead' version of the Newton-Dinkelbach method, a well-known technique for solving fractional and parametric optimization problems. This acceleration halves the Bregman divergence between the current…
We introduce a novel family of adaptive filtering algorithms based on a relative logarithmic cost. The new family intrinsically combines the higher and lower order measures of the error into a single continuous update based on the error…
We present a simple formula to update the pseudoinverse of a full-rank rectangular matrix that undergoes a low-rank modification, and demonstrate its utility for solving least squares problems. The resulting algorithm can be dramatically…
The Hildreth's algorithm is a row action method for solving large systems of inequalities. This algorithm is efficient for problems with sparse matrices, as opposed to direct methods such as Gaussian elimination or QR-factorization. We…
We present an Alternating Direction Method of Multipliers (ADMM) algorithm for solving optimization problems with an l_1 regularized least-squares cost function subject to recursive equality constraints. The considered optimization problem…
The robust adjustment of nonlinear models to data is considered in this paper. When data comes from real experiments, it is possible that measurement errors cause the appearance of discrepant values, which should be ignored when adjusting…
Randomized matrix compression techniques, such as the Johnson-Lindenstrauss transform, have emerged as an effective and practical way for solving large-scale problems efficiently. With a focus on computational efficiency, however, forsaking…
Semidefinite programming (SDP) is a central topic in mathematical optimization with extensive studies on its efficient solvers. In this paper, we present a proof-of-principle sublinear-time algorithm for solving SDPs with low-rank…
This paper studies sparse nonlinear least squares problems, where the Jacobian matrices are unavailable or expensive to compute, yet have some underlying sparse structures. We construct the Jacobian models by the $ \ell_1 $ minimization…
The modern ability to collect vast quantities of data poses a challenge for parameter estimation problems. When posed as a nonlinear least squares problem fitting a model to data, the cost of each iteration grows linearly with the amount of…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
In this work, we deal with rank-constrained integer least-squares optimization problems arising in low-rank matrix factorization related applications. We propose a solution for constrained integer least-squares problem subject to equality,…
In this paper, a novel quadratic convex optimal power flow model, namely, MDOPF, is proposed to determine the optimal dispatches of distributed generators. Based on the results of MDOPF, two price mechanisms, distribution locational…
Image restoration is typically addressed through non-convex inverse problems, which are often solved using first-order block-wise splitting methods. In this paper, we consider a general type of non-convex optimisation model that captures…
This paper introduces a novel framework for matrix diagonalization, recasting it as a sequential decision-making problem and applying the power of Decision Transformers (DTs). Our approach determines optimal pivot selection during…
The least square solution of minimum norm of a rectangular linear system of equations can be found out iteratively by using matrix splittings. However, the convergence of such an iteration scheme arising out of a matrix splitting is…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…