Proximity in 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...

Integer Quadratic Programming Models in Computational Biology

This presentation has two purposes: (1) show operations researchers how they can apply quadratic binary programming to current problems in molecular biology, and (2) show formulations of some combinatorial optimization problems as integer programs. The former purpose is primary, and I wish to persuade researchers to enter this exciting frontier. The latter purpose is part of a work in progress....

Integer quadratic programming in the plane

Mixed-integer Quadratic Programming is in NP

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 that if the decision version of mixed-inte...