Mixed-integer Quadratic Programming is in NP

Mixed-integer quadratic programming 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-integer quadratic programming is feasible, then there exists a solution of polynomial size. This result generalizes and unifies classical results that quadratic programming is in NP and integer linear programming is in NP

Bit Representation Can Improve SDP Relaxations of Mixed-Integer Quadratic Programs

A standard trick in integer programming is to replace bounded integer variables with binary variables, using a bit representation. In a previous paper, we showed that this process can be used to improve linear programming relaxations of mixed-integer quadratic programs. In this paper, we show that it can also be used to improve {\em semidefinite}\/ programming relaxations

E.P. v. Alaska Psychiatric Institute: The Evolution of Involuntary Civil Commitments from Treatment to Punishment

Addresses the problem of identification of hybrid dynamical systems, by focusing the attention on hinging hyperplanes and Wiener piecewise affine autoregressive exogenous models. In particular, we provide algorithms based on mixed-integer linear or quadratic programming which are guaranteed to converge to a global optimu