Related papers: Two-parameter TSCSP method for solving complex sym…
This paper addresses non-convex constrained optimization problems that are characterized by a scalar complicating constraint. We propose an iterative bisection method for the dual problem (DualBi Algorithm) that recovers a feasible primal…
In this paper we examine iterative methods for solving the forward ($A{\bf x}={\bf b}$) and adjoint ($A^{T}{\bf y}={\bf g}$) systems of linear equations used to approximate the scattering amplitude, defined by ${\bf g}^{T}{\bf x}={\bf…
This paper analyzes a two-timescale stochastic algorithm framework for bilevel optimization. Bilevel optimization is a class of problems which exhibit a two-level structure, and its goal is to minimize an outer objective function with…
This paper expands the Cyclic Block Proximal Gradient method for block separable composite minimization by allowing for inexactly computed gradients and proximal maps. The resultant algorithm, the Inexact Cyclic Block Proximal Gradient…
Multi-block separable convex problems recently received considerable attention. This class of optimization problems minimizes a separable convex objective function with linear constraints. The algorithmic challenges come from the fact that…
We present two theoretical results on the computation of lambda-contractive sets for linear systems with state and input constraints. First, we show that it is possible to a priori compute a number of iterations that is sufficient to…
In the development of industrial digital twins, the optimization problem of technological and business processes often arises. In many cases, this problem can be reduced to a large-scale linear programming (LP) problem. The article is…
The Half-Space Matching (HSM) method has recently been developed as a new method for the solution of 2D scattering problems with complex backgrounds, providing an alternative to Perfectly Matched Layers (PML) or other artificial boundary…
Two-level stochastic optimization formulations have become instrumental in a number of machine learning contexts such as continual learning, neural architecture search, adversarial learning, and hyperparameter tuning. Practical stochastic…
Large sample size brings the computation bottleneck for modern data analysis. Subsampling is one of efficient strategies to handle this problem. In previous studies, researchers make more fo- cus on subsampling with replacement (SSR) than…
This paper discusses a class of thresholding-based iterative selection procedures (TISP) for model selection and shrinkage. People have long before noticed the weakness of the convex $l_1$-constraint (or the soft-thresholding) in wavelets…
This paper proposes a dual divide-and-optimize algorithm (DualOpt) for solving the large-scale traveling salesman problem (TSP). DualOpt combines two complementary strategies to improve both solution quality and computational efficiency.…
We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…
We introduce an extension of Stochastic Dual Dynamic Programming (SDDP) to solve stochastic convex dynamic programming equations. This extension applies when some or all primal and dual subproblems to be solved along the forward and…
The multiple scattering method T-matrix (MSTMM) can be used to solve the electromagnetic response of systems consisting of many compact scatterers, retaining a good level of accuracy while using relatively few degrees of freedom, largely…
We propose a two-level iterative scheme for solving general sparse linear systems. The proposed scheme consists of a sparse preconditioner that increases the skew-symmetric part and makes the main diagonal of the coefficient matrix as close…
In this paper, by regarding the two-subspace Kaczmarz method [20] as an alternated inertial randomized Kaczmarz algorithm we present a new convergence rate estimate which is shown to be better than that in [20] under a mild condition.…
In this paper we study dispersive wave equation using the method of multiple scales (MMS) and perform several numerical tests to investigate its accuracy. The key feature of our MMS solution is the linearity of the amplitude equation and…
For a linear complementarity problem, we present a relaxaiton accelerated two-sweep matrix splitting iteration method. The convergence analysis illustrates that the proposed method converges to the exact solution of the linear…
Model selection in the large-P small-N scenario is discussed in the framework of two-stage models. Two specific models are considered, namely, two-stage least squares (TSLS) involving instrumental variables (IVs), and mediation models. In…