Abstract

We consider nonconvex conic optimization that covers Standard Nonlinear Programming, Semidefinite Programming, Second Order Cone Programming. To the dual Lagrangian problem, we associate a relaxed primal convex problem, and give bounds for the duality gap. Then we propose a proximal extension of the column generation method of Dantzig-Wolfe algorithm (PECGM) which provides these bounds if we suppose in addition Slater's condition. Finally new applications are given in order to make implementable the step of PECGM for which a nonconvex program is supposed to be solved numerically.

Author information

Contact details are reproduced from the original publication and may be historical.

Alfred Auslender

Institut Camille Jordan, Université Claude Bernard, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne - Lyon, France
and: Département d'Economie, Ecole Polytechnique, Palaiseau, France

Keywords

  • Standard nonlinear programming
  • semidefinite programming
  • second order cone programming
  • duality gap
  • generation column algorithm
  • proximal method

Suggested citation

A. Auslender. “A Proximal Extension of the Column Generation Method to Nonconvex Conic Optimization Providing Bounds for the Duality Gap.” Journal of Convex Analysis 17 (2010), No. 3&4, 721–736. https://doi.org/10.68381/jca17048

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Published by Heldermann Verlag, 2010. Rights now held by Banach Press.