Related papers: Remark on the Smale's Problem 9
Linear complementarity problems provide a powerful framework to model nonsmooth phenomena in a variety of real-world applications. In dynamical control systems, they appear coupled to a linear input-output system in the form of linear…
In this paper, a class of general nonlinear programming problems with inequality and equality constraints is discussed. Firstly, the original problem is transformed into an associated simpler equivalent problem with only inequality…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
In this paper, we consider two formulations for Linear Matrix Inequalities (LMIs) under Slater type constraint qualification assumption, namely, SDP smooth and non-smooth formulations. We also propose two first-order linearly convergent…
Boundary problem for linear partial differential algebraic equations system with multiple characteristic curves is considered. It is supposed that matrix-functions pencil of the system under consideration is smoothly equivalent to special…
Integer Linear Programming with $n$ binary variables and $m$ many $0/1$-constraints can be solved in time $2^{\tilde O(m^2)} \text{poly}(n)$ and it is open whether the dependence on $m$ is optimal. Several seemingly unrelated problems,…
We examine versions of the classical inequalities of Paley and Zygmund for functions of several variables. A sharp multiplier inclusion theorem and variants on the real line are obtained.
We study an assembly line balancing problem that occurs in sheltered worker centers for the disabled, where workers with very different characteristics are present. We are interested in the situation in which parallel assembly lines are…
By using a selective filtration argument, we prove that the satisfiability problem of the unimodal logic of density is in $EXPTIME$. By using a tableau-like approach, we prove that the satisfiability problem of the bimodal logic of weak…
In order to verify programs or hybrid systems, one often needs to prove that certain formulas are unsatisfiable. In this paper, we consider conjunctions of polynomial inequalities over the reals. Classical algorithms for deciding these not…
Finite linear least squares is one of the core problems of numerical linear algebra, with countless applications across science and engineering. Consequently, there is a rich and ongoing literature on algorithms for solving linear least…
Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help reduce the problem dimension, cut…
The demonstrated code-understanding capability of LLMs raises the question of whether they can be used for automated program verification, a task that demands high-level abstract reasoning about program properties that is challenging for…
The linearizability of differential equations was first considered by Lie for scalar second order semi-linear ordinary differential equations. Since then there has been considerable work done on the algebraic classification of linearizable…
We provide elementary and accurate numerical solutions to the differential-difference equation, which improves an explicit version of the linear sieve given by Nathanson.
A class of interior point methods using inexact directions is analysed. The linear system arising in interior point methods for linear programming is reformulated such that the solution is less sensitive to perturbations in the right-hand…
A Mathematica based program has been elaborated in order to determine the symmetry group of a finite difference equation, by means of its differential representation. The package provides functions which enable us to solve the determining…
The aim of this work is to develop general optimization methods for finite difference schemes used to approximate linear differential equations. The specific case of the transport equation is exposed. In particular, the minimization of the…
We propose an extremely versatile approach to address a large family of matrix nearness problems, possibly with additional linear constraints. Our method is based on splitting a matrix nearness problem into two nested optimization problems,…
We consider a class of systems of difference equations defined on an elementary quadrilateral of the ${\mathbb{Z}}^2$ lattice, define their eliminable and dynamical variables, and demonstrate their use. Using the existence of infinite…