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Matrix functions are utilized to rewrite smooth spectral constrained matrix optimization problems as smooth unconstrained problems over the set of symmetric matrices which are then solved via the cubic-regularized Newton method. A…
Non-smooth regularization is widely used in image reconstruction to eliminate the noise while preserving subtle image structures. In this work, we investigate the use of proximal Newton (PN) method to solve an optimization problem with a…
Stochastic second-order methods achieve fast local convergence in strongly convex optimization by using noisy Hessian estimates to precondition the gradient. However, these methods typically reach superlinear convergence only when the…
A collection of codes (in MATLAB & Fortran 77), and examples, for solving reaction-diffusion equations in one and two space dimensions is presented. In areas of the mathematical community spectral methods are used to remove the stiffness…
We describe an exact and highly efficient numerical algorithm for solving a special but important class of convection-diffusion equations. These equations occur in many problems in physics, chemistry, or biology, and they are usually hard…
We propose a Hermite spectral method for the inelastic Boltzmann equation, which makes two-dimensional periodic problem computation affordable by the hardware nowadays. The new algorithm is based on a Hermite expansion, where the expansion…
This paper presents a novel approach to solving large-scale minimax problems with nonsmooth regularizers. We propose a stochastic implicit proximal point algorithm with variance reduction techniques where stochastic oracles are selected in…
The work reported in this article presents a high-order, stable, and efficient Gegenbauer pseudospectral method to solve numerically a wide variety of mathematical models. The proposed numerical scheme exploits the stability and the…
A spectral method is developed for the direct solution of linear ordinary differential equations with variable coefficients. The method leads to matrices which are almost banded, and a numerical solver is presented that takes O(m^2n)…
Spectral estimation can be preformed using the so called THREE-like approach. Such method leads to a convex optimization problem whose solution is characterized through its dual problem. In this paper, we show that the dual problem can be…
We present a computationally efficient algorithm for stable numerical differentiation from noisy, uniformly-sampled data on a bounded interval. The method combines multi-interval Fourier extension approximations with an adaptive domain…
We develop an accelerated gradient descent algorithm on the Grassmann manifold to compute the subspace spanned by a number of leading eigenvectors of a symmetric positive semi-definite matrix. This has a constant cost per iteration and a…
The use of implicit time-stepping schemes for the numerical approximation of solutions to stiff nonlinear time-evolution equations brings well-known advantages including, typically, better stability behaviour and corresponding support of…
This work investigates the parameter estimation performance of super-resolution line spectral estimation using atomic norm minimization. The focus is on analyzing the algorithm's accuracy of inferring the frequencies and complex magnitudes…
We develop a computationally efficient algorithm for the automatic regularization of nonlinear inverse problems based on the discrepancy principle. We formulate the problem as an equality constrained optimization problem, where the…
In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned…
In this paper, we consider an unconstrained optimization model where the objective is a sum of a large number of possibly nonconvex functions, though overall the objective is assumed to be smooth and convex. Our bid to solving such model…
We consider the inverse acoustic obstacle problem for sound-soft star-shaped obstacles in two dimensions wherein the boundary of the obstacle is determined from measurements of the scattered field at a collection of receivers outside the…
Model reduction methods often aim at an identification of slow invariant manifolds in the state space of dynamical systems modeled by ordinary differential equations. We present a predictor corrector method for a fast solution of an…
Many data-fitting applications require the solution of an optimization problem involving a sum of large number of functions of high dimensional parameter. Here, we consider the problem of minimizing a sum of $n$ functions over a convex…