Related papers: An RADI-type method for stochastic continuous-time…
In this paper, we propose a stochastic method for solving equality constrained optimization problems that utilizes predictive variance reduction. Specifically, we develop a method based on the sequential quadratic programming paradigm that…
The residual cutting (RC) method has been proposed for efficiently solving linear equations obtained from elliptic partial differential equations. Based on the RC, we have introduced the generalized residual cutting (GRC) method, which can…
We propose a higher-order dimensionality reduction framework based on the Trace Ratio (TR) optimization problem. We establish conditions for existence and uniqueness of solutions and clarify the theoretical connection between the Trace…
Stochastic optimisation problems minimise expectations of random cost functions. We use 'optimise then discretise' method to solve stochastic optimisation. In our approach, accurate quadrature methods are required to calculate the…
A method of prediction is presented to aid compression of sequences of complex-valued samples. The focus is on using prediction to reduce the average magnitude of residual values after prediction (not on the subsequent compression of the…
In this paper, we propose high-order numerical methods for the Riesz space fractional advection-dispersion equations (RSFADE) on a {f}inite domain. The RSFADE is obtained from the standard advection-dispersion equation by replacing the…
We present a novel solution method for It\^o stochastic differential equations (SDEs). We subdivide the time interval into sub-intervals, then we use the quadratic polynomials for the approximation between two successive intervals. The main…
Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…
We explore order reduction techniques for solving the algebraic Riccati equation (ARE), and investigating the numerical solution of the linear-quadratic regulator problem (LQR). A classical approach is to build a surrogate low dimensional…
In this paper, we consider a class of nonconvex-linear minimax problems on Riemannian manifolds, which find wide applications in machine learning and signal processing. For solving this class of problems, we develop a flexible Riemannian…
In this note, we present a new numerical method for solving backward stochastic differential equations. Our method can be viewed as an analogue of the classical finite element method solving deterministic partial differential equations.
A class of (block) rational Krylov subspace based projection method for solving large-scale continuous-time algebraic Riccati equation (CARE) $0 = \mathcal{R}(X) := A^HX + XA + C^HC - XBB^HX$ with a large, sparse $A$ and $B$ and $C$ of full…
This work introduces a novel approach for data-driven model reduction of time-dependent parametric partial differential equations. Using a multi-step procedure consisting of proper orthogonal decomposition, dynamic mode decomposition and…
In this paper we discuss how to decompose the constrained generalized discrete-time algebraic Riccati equation arising in optimal control and optimal filtering problems into two parts corresponding to an additive decomposition X=X0+D of…
We propose a Riemannian version of Nesterov's Accelerated Gradient algorithm (RAGD), and show that for geodesically smooth and strongly convex problems, within a neighborhood of the minimizer whose radius depends on the condition number as…
We study a multigrid method for solving large linear systems of equations with tensor product structure. Such systems are obtained from stochastic finite element discretization of stochastic partial differential equations such as the…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…
In this paper, we propose a StochAstic Recursive grAdient algoritHm (SARAH), as well as its practical variant SARAH+, as a novel approach to the finite-sum minimization problems. Different from the vanilla SGD and other modern stochastic…
The efficient solution of large-scale multiterm linear matrix equations is a challenging task in numerical linear algebra, and it is a largely open problem. We propose a new iterative scheme for symmetric and positive definite operators,…
A new algorithm is proposed to accelerate RANSAC model quality calculations. The method is based on partitioning the joint correspondence space, e.g., 2D-2D point correspondences, into a pair of regular grids. The grid cells are mapped by…