Related papers: Splitted Levenberg-Marquardt Method for Large-Scal…
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…
Recently, a Levenberg-Marquardt method with Singular Scaling matrix, called LMMSS, was proposed and successfully applied in parameter estimation in heat conduction problems, where the choice of suitable singular scaling matrix resulted in…
The Levenberg-Marquardt algorithm is one of the most popular algorithms for finding the solution of nonlinear least squares problems. Across different modified variations of the basic procedure, the algorithm enjoys global convergence, a…
A new Levenberg--Marquardt (LM) method for solving nonlinear least squares problems with convex constraints is described. Various versions of the LM method have been proposed, their main differences being in the choice of a damping…
Low complexity of a system model is essential for its use in real-time applications. However, sparse identification methods commonly have stringent requirements that exclude them from being applied in an industrial setting. In this paper,…
Inspired by certain regularization techniques for linear inverse problems, in this work we investigate the convergence properties of the Levenberg-Marquardt method using singular scaling matrices. Under a completeness condition, we show…
In this paper, we first propose a new Levenberg-Marquardt method for solving constrained (and not necessarily square) nonlinear systems. Basically, the method combines the unconstrained Levenberg-Marquardt method with a type of feasible…
Least squares form one of the most prominent classes of optimization problems, with numerous applications in scientific computing and data fitting. When such formulations aim at modeling complex systems, the optimization process must…
The sparse generalized eigenvalue problem arises in a number of standard and modern statistical learning models, including sparse principal component analysis, sparse Fisher discriminant analysis, and sparse canonical correlation analysis.…
This paper is concerned with the approximation of the solution of partial differential equations by means of artificial neural networks. Here a feedforward neural network is used to approximate the solution of the partial differential…
The Levenberg-Marquardt algorithm is a flexible iterative procedure used to solve non-linear least squares problems. In this work we study how a class of possible adaptations of this procedure can be used to solve maximum likelihood…
Motivated by localization problems such as cadastral maps refinements, we consider a generic Nonlinear Least Squares (NLS) problem of minimizing an aggregate squared fit across all nonlinear equations (measurements) with respect to the set…
In this paper, we revisit the classical problem of solving over-determined systems of nonsmooth equations numerically. We suggest a nonsmooth Levenberg--Marquardt method for its solution which, in contrast to the existing literature, does…
Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…
We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program. Such problems occur naturally in many scientific and web applications. Although there are efficient methods which tackle this problem, they are…
This paper proposes a sparse regression strategy for discovery of ordinary differential equations from incomplete and noisy data. Inference is performed over both equation parameters and state variables using a statistically motivated…
This paper is about how to partition decision variables while decomposing a large-scale optimization problem for the best performance of distributed solution methods. Solving a large-scale optimization problem sequen- tially can be…
A nonlinear generalisation of the PageRank problem involving the Moore-Penrose inverse of an incidence matrix is developed for local graph partitioning purposes. The Levenberg-Marquardt method with a full rank Jacobian variant provides a…
This paper presents an algorithm for sampling random variables that allows to separation of the sampling process into subproblems by dividing the sample space into overlapping parts. The subproblems can be solved independently of each other…
In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…