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We present a polynomial-time algorithm that obtains a set of Asymptotic Linear Programs (ALPs) from a given linear system S, such that one of these ALPs admits a feasible solution if and only if S admits a feasible solution. We also show…
We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…
Polynomial optimization problems over binary variables can be expressed as integer programs using a linearization with extra monomials in addition to those arising in the given polynomial. We characterize when such a linearization yields an…
Much algorithmic research in NLP aims to efficiently manipulate rich formal structures. An algorithm designer typically seeks to provide guarantees about their proposed algorithm -- for example, that its running time or space complexity is…
Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operations research, and optimization. Despite the consistent efforts on this problem, all…
We consider a recently introduced fair repetitive scheduling problem involving a set of clients, each asking for their associated job to be daily scheduled on a single machine across a finite planning horizon. The goal is to determine a job…
In this work, we propose an optimization framework for estimating a sparse robust one-dimensional subspace. Our objective is to minimize both the representation error and the penalty, in terms of the l1-norm criterion. Given that the…
Given an integer mxn matrix A satisfying certain regularity assumptions, a well-known integer programming problem asks to find an integer point in the associated knapsack polytope P(A, b)={x: A x= b, x>=0} or determine that no such point…
In this article, we introduce a new technique for precision tuning. This problem consists of finding the least data types for numerical values such that the result of the computation satisfies some accuracy requirement. State of the art…
Interior-point algorithms constitute a very interesting class of algorithms for solving linear-programming problems. In this paper we study efficient implementations of such algorithms for solving the linear program that appears in the…
Integer linear programs (ILPs) are a widely applied framework for dealing with combinatorial problems that arise in practice. It is known, e.g., by the success of CPLEX, that preprocessing and simplification can greatly speed up the process…
In this paper, we give an algorithm that finds an epsilon-approximate solution to a mixed integer quadratic programming (MIQP) problem. The algorithm runs in polynomial time if the rank of the quadratic function and the number of integer…
This paper presents the first study of the complexity of the optimization problem for integer linear-exponential programs which extend classical integer linear programs with the exponential function $x \mapsto 2^x$ and the remainder…
We give a strongly polynomial-time algorithm for integer linear programs defined by integer coefficient matrices whose subdeterminants are bounded by a constant and that contain at most two nonzero entries in each row. The core of our…
This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of…
In this paper, we present a polynomial-sized linear programming formulation of the Quadratic Assignment Problem (QAP). The proposed linear program is a network flow-based model. Hence, it provides for the solution of the QAP in polynomial…
We determine the maximal gap between the optimal values of an integer program and its linear programming relaxation, where the matrix and cost function are fixed but the right hand side is unspecified. Our formula involves irreducible…
For several decades the dominant techniques for integer linear programming have been branching and cutting planes. Recently, several authors have developed core point methods for solving symmetric integer linear programs (ILPs). An integer…