Mixed-integer quadratic programming reformulations of multi-task learning models

Multi-Quadratic Integer Programming: Models and Applications

Linear Reformulations of Integer Quadratic Programs

Let (QP ) be an integer quadratic program that consists in minimizing a quadratic function subject to linear constraints. In this paper, we present several linearizations of (QP ). Many linearization methods for the quadratic 0-1 programs are known. A natural approach when considering (QP ) is to reformulate it into a quadratic 0-1 program. However, this method, that we denote BBL (Binary Binar...

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...

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....

Formulations and Reformulations in Integer Programming

Creating good integer programming formulations had, as a basic axiom, the rule “Find formulations with tighter linear relaxations”. This rule, while useful when using unsophisticated branch-and-bound codes,is insufficient when using state-of-the-art codes that understand and embed many of the obvious formulation improvements. As these optimization codes become more sophisticated it is important...