Lagrangian Decomposition of Mixed-IntegerAll-Quadratic Programs

Ivo Nowak

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 22 pages

MSC 2000

90C11 Mixed integer programming
90C22 Semidefinite programming
Abstract

The purpose of this paper is threefold. First we show that the Lagrangian dual of a block-separable mixed-integer all-quadratic program (MIQQP) can be formulated as an eigenvalue optimization problem keeping the block-separable structure. Second we propose splitting schemes for reformulating non-separable problems as block-separable problems. Finally we report numerical results on solving the eigenvalue optimization problem by a proximal bundle algorithm applying Lagrangian decomposition. The results indicate that appropriate block-separable reformulations of MIQQPs could accelerate the running time of dual solution algorithms considerably.

Keywords:semidefinite programming,quadratic programming,combinatorial optimization,non-convex programming,decomposition