Related papers: A Bound for the Number of Different Basic Solution…
This paper deals with the polynomial linear system solving with errors (PLSwE) problem. Specifically, we focus on the evaluation-interpolation technique for solving polynomial linear systems and we assume that errors can occur in the…
We propose a randomized method for solving linear programs with a large number of columns but a relatively small number of constraints. Since enumerating all the columns is usually unrealistic, such linear programs are commonly solved by…
In semidefinite programming a proposed optimal solution may be quite poor in spite of having sufficiently small residual in the optimality conditions. This issue may be framed in terms of the discrepancy between forward error (the…
Recent successes of game-theoretic formulations in ML have caused a resurgence of research interest in differentiable games. Overwhelmingly, that research focuses on methods and upper bounds on their speed of convergence. In this work, we…
This short note provides and proves an easy algorithm to find a basic feasible solution for the Simplex Algorithm. The method uses a rule similar to Bland's rule for the initial phase of the algorithm.
The simplex method is one of the most fundamental technologies for solving linear programming (LP) problems and has been widely applied to different practical applications. In the past literature, how to improve and accelerate the simplex…
We introduce and study minimal (with respect to inclusion) solutions of systems of tropical linear differential equations. We describe the set of all minimal solutions for a single equation. It is shown that any tropical linear differential…
We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…
Linear superiorization considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not…
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…
One of my recent papers transforms an NP-Complete problem into the question of whether or not a feasible real solution exists to some Linear Program. The unique feature of this Linear Program is that though there is no explicit bound on the…
This paper investigates and bounds the expected solution quality of combinatorial optimization problems when feasible solutions are chosen at random. Loose general bounds are discovered, as well as families of combinatorial optimization…
We conjecture that if a system S \subseteq {x_i=1, x_i+x_j=x_k, x_i \cdot x_j=x_k: i,j,k \in {1,...,n}} has only finitely many solutions in integers x_1,...,x_n, then each such solution (x_1,...,x_n) satisfies |x_1|,...,|x_n| \leq…
Instances generation is crucial for linear programming algorithms, which is necessary either to find the optimal pivot rules by training learning method or to evaluate and verify corresponding algorithms. This study proposes a general…
We solve two long-standing open problems on word equations. Firstly, we prove that a one-variable word equation with constants has either at most three or an infinite number of solutions. The existence of such a bound had been conjectured,…
This thesis addresses the question of the maximal number of $d$-simplices for a simplicial complex which is embeddable into $\mathbb{R}^r$ for some $d \leq r \leq 2d$. A lower bound of $f_d(C_{r + 1}(n)) =…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Consider the problem of minimizing the sum of a smooth convex function and a separable nonsmooth convex function subject to linear coupling constraints. Problems of this form arise in many contemporary applications including signal…
We prove a linear bound on the average total curvature of the central path of linear programming theory in terms on the number of independent variables of the primal problem, and independent on the number of constraints.
Suppose that a solution $\widetilde{\mathbf{x}}$ to an underdetermined linear system $\mathbf{b} = \mathbf{A} \mathbf{x}$ is given. $\widetilde{\mathbf{x}}$ is approximately sparse meaning that it has a few large components compared to…