Subdeterminants and Concave Integer Quadratic Programming

On Approximation Algorithms for Concave Mixed-Integer Quadratic Programming

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 two algorithms that find an -approximate solution to a Concave Mixed-Integer Quadratic Programming problem. The running time of the proposed algorithms is polynomial in the size of the problem and in 1/ , provided ...

Concave Quadratic Cuts for Mixed-Integer Quadratic Problems

The technique of semidefinite programming (SDP) relaxation can be used to obtain a nontrivial bound on the optimal value of a nonconvex quadratically constrained quadratic program (QCQP). We explore concave quadratic inequalities that hold for any vector in the integer lattice Z, and show that adding these inequalities to a mixed-integer nonconvex QCQP can improve the SDP-based bound on the opt...

Quadratic Integer Programming: Complexity and Equivalent Forms

Parameterized Integer Quadratic Programming: Variables and Coefficients

In the Integer Quadratic Programming problem input is an n× n integer matrix Q, an m × n integer matrix A and an m-dimensional integer vector b. The task is to find a vector x ∈ Z minimizing xQx, subject to Ax ≤ b. We give a fixed parameter tractable algorithm for Integer Quadratic Programming parameterized by n+α. Here α is the largest absolute value of an entry of Q and A. As an application o...

Integer Quadratic Programming for Control and Communication

The main topic of this thesis is integer quadratic programming with applications to prob-lems arising in the areas of automatic control and communication. One of the mostwidespread modern control methods is Model Predictive Control (MPC). In each sam-pling time, MPC requires the solution of a Quadratic Programming (QP) problem. Tobe able to use MPC for large systems, and at high...