Globally Solving Nonconvex QPs via Completely Positive Programming

TitleGlobally Solving Nonconvex QPs via Completely Positive Programming
Publication TypeJournal Article
Year of Publication2011
AuthorsChen, J, Burer, S
JournalMathematical Programming Computation
Date Published02/2011
Other NumbersANL/MCS-P1837-0211

Nonconvex quadratic programming is an NP-hard problem that optimizes a general quadratic function over linear constraints. This paper introduces a new global optimization algorithm for this problem, which combines two ideas from the literature|nite branching based on the first-order KKT conditions and polyhedral-semidefinite relaxations of completely positive (or copositive) programs. Through a series of computational experiments comparing the new algorithm with existing codes on a diverse set of test instances, we demonstrate that the new algorithm is an attractive method for globally solving nonconvex QP.