Related papers: Least Sqaure Method for Sum of the Functions Satys…
We study a class of combinatorial scheduling problems characterized by a particular type of constraint often associated with electrical power or gas energy. This constraint appears in several practical applications and is expressed as a sum…
Least squares is by far the simplest and most commonly applied computational method in many fields. In almost all applications, the least squares objective is rarely the true objective. We account for this discrepancy by parametrizing the…
Many combinatorial optimisation problems can be modelled as valued constraint satisfaction problems. In this paper, we present a polynomial-time algorithm solving the valued constraint satisfaction problem for a fixed number of variables…
In this paper we propose a new approach to least squares approximation problems. This approach is based on partitioning and Schur function. The nature of this approach is combinatorial, while most existing approaches are based on algebra…
We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels. Given a sufficiently large (polynomial-size) training set drawn i.i.d. from…
This paper studies adaptive least-squares finite element methods for convection-dominated diffusion-reaction problems. The least-squares methods are based on the first-order system of the primal and dual variables with various ways of…
When a physical system is modeled by a nonlinear function, the unknown parameters can be estimated by fitting experimental observations by a least-squares approach. Newton's method and its variants are often used to solve problems of this…
We present an algorithm for computing sparse, least squares-based polynomial chaos expansions, incorporating both adaptive polynomial bases and sequential experimental designs. The algorithm is employed to approximate stochastic…
We propose a new prediction method for multivariate linear regression problems where the number of features is less than the sample size but the number of outcomes is extremely large. Many popular procedures, such as penalized regression…
In this work we present a new simple but efficient scheme - Subsquares approach - for development of algorithms for enclosing the solution set of overdetermined interval linear systems. We are going to show two algorithms based on this…
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…
We introduce a new fundamental algorithm called Matrix-POAFD to solve the matrix least square problem. The method is based on the matching pursuit principle. The method directly extracts, among the given features as column vectors of the…
We present a new algorithm for solving a polynomial program P based on the recent "joint + marginal" approach of the first author for, parametric optimization. The idea is to first consider the variable x1 as a parameter and solve the…
We propose a new polynomial-time algorithm for linear programming. We further extend the ideas used in this new linear programming algorithm for nonlinear programming problems. The new algorithm is based on the idea of treating the…
In this work, we propose a novel discrete-time distributed algorithm for finding least-squares solutions of linear algebraic equations with a scheduling protocol to further enhance its scalability. Each agent in the network is assumed to…
In this paper, we study the problem of finding the least square solutions of over-determined linear algebraic equations over networks in a distributed manner. Each node has access to one of the linear equations and holds a dynamic state. We…
Submodular functions describe a variety of discrete problems in machine learning, signal processing, and computer vision. However, minimizing submodular functions poses a number of algorithmic challenges. Recent work introduced an…
The purpose of the paper is to provide a characterization of the error of the best polynomial approximation of composite functions in weighted spaces. Such a characterization is essential for the convergence analysis of numerical methods…
A method for moving least squares interpolation and differentiation is presented in the framework of orthogonal polynomials on discrete points. This yields a robust and efficient method which can avoid singularities and breakdowns in the…
We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…