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Rapport (Rapport De Recherche) Année : 2010

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

Jérôme Malick

Résumé

This paper presents new semidefinite programming bounds for 0-1 quadratic problems with linear or quadratic constraints. These bounds are obtained by Lagrangian duality and convex optimization; and they have interesting numerical features: the tightness is improved by Newton-like method, and the final accuracy level is controlled by real parameter acting like a cursor. This gives ways to trade computing time for a (small) deterioration of the quality of the usual semidefinite bounds, in view of enhancing this efficiency in exact resolution schemes. The numerical properties are illustrated on standard test-problems (unconstrained 0-1 quadratic problems, heaviest k-subgraphs problems, and graph bisection problems). Extensive comparisons with usual bounds (obtained by linear, quadratic or semidefinite programming) are provided on those problems.
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Dates et versions

hal-01125760 , version 1 (06-03-2015)

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  • HAL Id : hal-01125760 , version 1

Citer

Jérôme Malick, Frédéric Roupin. On the bridge between combinatorial optimization and nonlinear optimization: new semidefinite bounds for 0-1 quadratic problems leading to Newton methods. [Research Report] CEDRIC-10-1924, CEDRIC Lab/CNAM. 2010. ⟨hal-01125760⟩
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