相关论文: Convergence and Near-optimal Sampling for Multivar…
In this paper, we address a manifold constrained nonsmooth optimization problem involving the composition of a weakly convex function and a smooth mapping under the availability of a parametrization of the manifold. To find a stationary…
We consider minimizing $f(x) = \mathbb{E}[f(x,\omega)]$ when $f(x,\omega)$ is possibly nonsmooth and either strongly convex or convex in $x$. (I) Strongly convex. When $f(x,\omega)$ is $\mu-$strongly convex in $x$, we propose a variable…
We propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation frame- work. Our method is motivated by generalized Polynomial…
Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a…
In approximation of functions based on point values, least-squares methods provide more stability than interpolation, at the expense of increasing the sampling budget. We show that near-optimal approximation error can nevertheless be…
In this research, we solve polynomial, Sobolev polynomial, rational, and Sobolev rational least squares problems. Although the increase in the approximation degree allows us to fit the data better in attacking least squares problems, the…
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,…
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…
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…
Functions with discontinuities appear in many applications such as image reconstruction, signal processing, optimal control problems, interface problems, engineering applications and so on. Accurate approximation and interpolation of these…
For a probability measure on a real separable Hilbert space, we are interested in "volume-based" approximations of the d-dimensional least squares error of it, i.e., least squares error with respect to a best fit d-dimensional affine…
The adaptive Antoulas-Anderson (AAA) algorithm for rational approximation is a widely used method for the efficient construction of highly accurate rational approximations to given data. While AAA can often produce rational approximations…
In this work, we study a random orthogonal projection based least squares estimator for the stable solution of a multivariate nonparametric regression (MNPR) problem. More precisely, given an integer $d\geq 1$ corresponding to the dimension…
This paper proposes a new computational method for solving structured least squares problems that arise in the process of identification of coherent structures in fluid flows. It is deployed in combination with dynamic mode decomposition…
In this note, we extend the Vandermonde with Arnoldi method recently advocated by P. D. Brubeck, Y. Nakatsukasa and L. N. Trefethen to dealing with the confluent Vandermonde matrix. To apply the Arnoldi process, it is critical to find a…
This paper concerns the approximation of smooth, high-dimensional functions from limited samples using polynomials. This task lies at the heart of many applications in computational science and engineering - notably, some of those arising…
We propose a methodology for computing single and multi-asset European option prices, and more generally expectations of scalar functions of (multivariate) random variables. This new approach combines the ability of Monte Carlo simulation…
Markov parameters play a key role in system identification. There exists many algorithms where these parameters are estimated using least-squares in a first, pre-processing, step, including subspace identification and multi-step…
Classical theory for quasi-Newton schemes has focused on smooth deterministic unconstrained optimization while recent forays into stochastic convex optimization have largely resided in smooth, unconstrained, and strongly convex regimes.…
Inverse Vandermonde matrix calculation is a long-standing problem to solve nonsingular linear system $Vc=b$ where the rows of a square matrix $V$ are constructed by progression of the power polynomials. It has many applications in…