Alberto Del Pia Concave Mixed-Integer Quadratic Programming is the problem of minimizing a concave quadratic polynomial over the mixed-integer points in a polyhedral region. In this work we describe an algorithm that finds an ε-approximate solution to a Concave Mixed-Integer Quadratic Programming problem. The running time of the proposed algorithm is polynomial in the size of the problem … Read more
In this paper we show that the diameter of a d-dimensional lattice polytope in [0,k]^n is at most (k – 1/2) d. This result implies that the diameter of a d-dimensional half-integral polytope is at most 3/2 d. We also show that for half-integral polytopes the latter bound is tight for any d. CitationUniversity of … Read more
We investigate a new class of congestion games, called Totally Unimodular Congestion Games, in which the strategies of each player are expressed as binary vectors lying in a polyhedron defined using a totally unimodular constraint matrix and an integer right-hand side. We study both the symmetric and the asymmetric variants of the game. In the … Read more
We study the polyhedral convex hull of a mixed-integer set S defined by a collection of multilinear equations over the 0-1-cube. Such sets appear frequently in the factorable reformulation of mixed-integer nonlinear optimization problems. In particular, the set S represents the feasible region of a linearized unconstrained binary polynomial optimization problem. We define an equivalent … Read more
We complete the complexity classification by degree of minimizing a polynomial in two variables over the integer points in a polyhedron. Previous work shows that in two variables, optimizing a quadratic polynomial over the integer points in a polyhedral region can be done in polynomial time, while optimizing a quartic polynomial in the same type … Read more
Mixed-integer quadratic programming (MIQP) is the problem of optimizing a quadratic function over points in a polyhedral set where some of the components are restricted to be integral. In this paper, we prove that the decision version of mixed-integer quadratic programming is in NP, thereby showing that it is NP-complete. This is established by showing … Read more