On the bridge between combinatorial optimization and nonlinear optimization: a family of semidefinite bounds for 0-1 quadratic problems leading to quasi-Newton methods.

This article presents a family of semidefinite programming bounds, obtained by Lagrangian duality, for 0-1 quadratic optimization problems with linear or quadratic constraints. These bounds have useful computational properties: they have a good ratio of tightness to computing time, they can be optimized by a quasi-Newton method, and their final tightness level is controlled by a real parameter. These properties are illustrated on three standard combinatorial optimization problems: unconstrained 0-1 quadratic optimization, heaviest $$k$$-subgraph, and graph bisection. [ABSTRACT FROM AUTHOR]