Related papers: On Chubanov's method for Linear Programming

We point out that Chubanov's oracle-based algorithm for linear programming [5] can be applied almost as it is to linear semi-infinite programming (LSIP). In this note, we describe the details and prove the polynomial complexity of the…

We consider the stability analysis of a large class of linear 1-D PDEs with polynomial data. This class of PDEs contains, as examples, parabolic and hyperbolic PDEs, PDEs with boundary feedback and systems of in-domain/boundary coupled…

It is well known that the most challenging question in optimization and discrete geometry is whether there is a strongly polynomial time simplex algorithm for linear programs (LPs). This paper gives a positive answer to this question by…

Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…

In this paper we develop a very special substitution method for solving a general linear programming problem (LPP). Of course the substitution is a kind of elimination of variable but this method must not be confused with the so-called…

We address the problem of testing weak optimality of a given solution of a given interval linear program. The problem was recently wrongly stated to be polynomially solvable. We disprove it. We show that the problem is NP-hard in general.…

We study optimal decision policies for integer linear programs with a fixed feasible set and varying cost vectors, represented as linear decision trees. Once synthesized for a given feasible set, they return an optimal solution for any…

We present a polynomial-time algorithm that determines, given some choice rule, whether there exists an obviously strategy-proof mechanism for that choice rule.

We give the first algorithm for testing the feasibility of a system of sporadic real-time tasks on a set of identical processors, solving one major open problem in the area of multiprocessor real-time scheduling [S.K. Baruah and K. Pruhs,…

This paper is aimed to prove the strong duality theorem for continuous-time linear programming problems in which the coefficients are assumed to be piecewise continuous functions. The previous paper proved the strong duality theorem for the…

We study the computational complexity of fundamental problems over the $p$-adic numbers ${\mathbb Q}_p$ and the $p$-adic integers ${\mathbb Z}_p$. Gu\'epin, Haase, and Worrell proved that checking satisfiability of systems of linear…

We study here several variants of the covariates fine balance problem where we generalize some of these problems and introduce a number of others. We present here a comprehensive complexity study of the covariates problems providing…

We present a deterministic polynomial-time algorithm that solves the 3-satisfiability problem.

We present a novel way of generating Lyapunov functions for proving linear convergence rates of first-order optimization methods. Our approach provably obtains the fastest linear convergence rate that can be verified by a quadratic Lyapunov…

This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…

In a recent paper by S. Gubin [cs/0701023v1], a polynomial-time solution to the 3SAT problem was presented as proof that P=NP. The proposed algorithm cannot be made to work, which I shall demonstrate.

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…

First-order methods are often analyzed via their continuous-time models, where their worst-case convergence properties are usually approached via Lyapunov functions. In this work, we provide a systematic and principled approach to find and…

This paper studies, for the first time, a bilevel polynomial program whose constraints involve uncertain linear constraints and another uncertain linear optimization problem. In the case of box data uncertainty, we present a sum of squares…

Markov decision processes (MDPs) are a fundamental model in sequential decision making. Robust MDPs (RMDPs) extend this framework by allowing uncertainty in transition probabilities and optimizing against the worst-case realization of that…