Related papers: Binary Solutions for Overdetermined Systems of Lin…
Non-linear polynomial systems over finite fields are used to model functional behavior of cryptosystems, with applications in system security, computer cryptography, and post-quantum cryptography. Solving polynomial systems is also one of…
In this paper, we propose and analyze an inexact version of the symmetric proximal alternating direction method of multipliers (ADMM) for solving linearly constrained optimization problems. Basically, the method allows its first subproblem…
We consider the problem of robust matrix completion, which aims to recover a low rank matrix $L_*$ and a sparse matrix $S_*$ from incomplete observations of their sum $M=L_*+S_*\in\mathbb{R}^{m\times n}$. Algorithmically, the robust matrix…
In this paper by exploiting critical point theory, the existence of two distinct nontrivial solutions for a nonlinear algebraic system with a parameter is established. Our goal is achieved by requiring an appropriate behavior of the…
In this paper we introduce an algorithm for determining the orbital elements and individual masses of visual binaries. The algorithm uses an optimal point, which minimizes a specific function describing the average length between the…
This work introduces a multidimensional generalization of the maximum bisection problem. A mixed integer linear programming formulation is proposed with the proof of its correctness. The numerical tests, made on the randomly generated…
Consider the $n$th degree polynomial equation, $X^n+A_{n-1}X^{n-1}+...+A_1X+A_0=0$ over the ring of 2 by 2 complex matrices. If this equation has more than ${2n \choose 2}$ solutions, then it has infinitely many solutions. We show here that…
This paper presents a majorized alternating direction method of multipliers (ADMM) with indefinite proximal terms for solving linearly constrained $2$-block convex composite optimization problems with each block in the objective being the…
A multigrid method is proposed for solving nonlinear eigenvalue problems by the finite element method. With this new scheme, solving nonlinear eigenvalue problem is decomposed to a series of solutions of linear boundary value problems on…
Alternating direction methods of multipliers (ADMMs) are popular approaches to handle large scale semidefinite programs that gained attention during the past decade. In this paper, we focus on solving doubly nonnegative programs (DNN),…
We present a new class of preconditioned iterative methods for solving linear systems of the form $Ax = b$. Our methods are based on constructing a low-rank Nystr\"om approximation to $A$ using sparse random matrix sketching. This…
Cut generation and lifting are key components for the performance of state-of-the-art mathematical programming solvers. This work proposes a new general cut-and-lift procedure that exploits the combinatorial structure of 0-1 problems via a…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
We prove that bounded solutions to an overdetermined fully nonlinear free boundary problem in the plane are one dimensional. Our proof relies on maximum principle techniques and convexity arguments.
In this paper, we address the identification problem for the systems characterized by linear time-invariant dynamics with bilinear observation models. More precisely, we consider a suitable parametric description of the system and formulate…
Two-stage stochastic programs with binary recourse are challenging to solve and efficient solution methods for such problems have been limited. In this work, we generalize an existing binary decision diagram-based (BDD-based) approach of…
We establish the existence of positive solutions to a general class of overdetermined semilinear elliptic boundary problems on suitable bounded open sets $\Omega\subset\mathbb{R}^n$. Specifically, for $n\leq 4$ and under mild technical…
We prove convergence with optimal algebraic rates for an adaptive finite element method for nonlinear equations with strongly monotone operator. Unlike prior works, our analysis also includes the iterative and inexact solution of the…
A quadratic dynamical system with practical applications is taken into considered. This system is transformed into a new bilinear system with Hadamard products by means of the implicit matrix structure. The corresponding quadratic bilinear…
A symbolic computational algorithm which detects " linear "` solutions of nonlinear polynomial differential equations of single functions, is developed throughout this paper.