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

Jérôme Malick 1 Frédéric Roupin 2
1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : 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.
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Article dans une revue
Mathematical Programming, Springer Verlag, 2013, 140 (1), pp.99-124. <10.1007/s10107-012-0628-6>
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Jérôme Malick, Frédéric Roupin. On the bridge between combinatorial optimization and nonlinear optimization: a family of semidefinite bounds for 0-1 quadratic problems leading to quasi-Newton methods. Mathematical Programming, Springer Verlag, 2013, 140 (1), pp.99-124. <10.1007/s10107-012-0628-6>. <hal-00662367>

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