相关论文: Computing the B\'ezier Control Points of the Lagra…

We made a comparative analysis of numerical methods for multidimensional optimization. The main parameter is a number of computations of the test function to reach necessary accuracy, as it is computationally "slow". For complex functions,…

New versions and extensions of Benson's outer approximation algorithm for solving linear vector optimization problems are presented. Primal and dual variants are provided in which only one scalar linear program has to be solved in each…

The goal of this paper is to survey the properties of the eigenvalue relaxation for least squares binary problems. This relaxation is a convex program which is obtained as the Lagrangian dual of the original problem with an implicit compact…

We investigate the following question: if a polynomial can be evaluated at rational points by a polynomial-time boolean algorithm, does it have a polynomial-size arithmetic circuit? We argue that this question is certainly difficult.…

The maximum volume principle is investigated as a means to solve the following problem: Given a set of arbitrary interpolation nodes, how to choose a set of polynomial basis functions for which the Lagrange interpolation problem is…

Lagrangian-based methods are classical methods for solving convex optimization problems with equality constraints. We present novel prediction-correction frameworks for such methods and their variants, which can achieve $O(1/k)$ non-ergodic…

Any square matrix can be transformed into a doubly stochastic matrix via Sinkhorn scaling with diagonal matrices or completing to a larger dimensional matrix. Standard Birkhoff-von Neumann and Pauli decompositions represent such matrices as…

The most common method for calculating accurate numerical solutions for complicated linear differential equations - for example, finding eigenvalues and eigenfunctions of the Schrodinger equation for many-electron atoms - is the variational…

The results on Vandermonde-like matrices were introduced as a generalization of polynomial Vandermonde matrices, and the displacement structure of these matrices was used to derive an inversion formula. In this paper we first present a fast…

An iterative randomness extraction algorithm which generalized the Von Neumann's extraction algorithm is detailed, analyzed and implemented in standard C++. Given a sequence of independently and identically distributed biased Bernoulli…

This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…

Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the…

We consider nondeterministic probabilistic programs with the most basic liveness property of termination. We present efficient methods for termination analysis of nondeterministic probabilistic programs with polynomial guards and…

The Augmented Lagrangian Method as an approach for regularizing inverse problems received much attention recently, e.g. under the name Bregman iteration in imaging. This work shows convergence (rates) for this method when Morozov's…

We consider the interpolation problem with the inverse multiquadric radial basis function. The problem usually produces a large dense linear system that has to be solved by iterative methods. The efficiency of such methods is strictly…

In computer aided geometric design a polynomial is usually represented in Bernstein form. The de Casteljau algorithm is the most well-known algorithm for evaluating a polynomial in this form. Evaluation via the de Casteljau algorithm has…

We prove a sharp Bernstein-type inequality for complex polynomials which are positive and satisfy a polynomial growth condition on the positive real axis. This leads to an improved upper estimate in the recent work of Culiuc and Treil on…

We consider the stochastic integrals of multivariate point processes and study their concentration phenomena. In particular, we obtain a Bernstein type of concentration inequality through Dol\'eans-Dade exponential formula and a uniform…

It is shown that the problem of balancing a nonnegative matrix by positive diagonal matrices can be recast as a constrained nonlinear multiparameter eigenvalue problem. Based on this equivalent formulation some adaptations of the power…

In this study, we introduce a novel methodological framework called Bayesian Penalized Empirical Likelihood (BPEL), designed to address the computational challenges inherent in empirical likelihood (EL) approaches. Our approach has two…