Decomposition and Nondifferentiable Optimization with the Projective Algorithm
AbstractThis paper deals with an application of a variant of Karmarkar's projective algorithm for linear programming to the solution of a generic nondifferentiable minimization problem. This problem is closely related to the Dantzig-Wolfe decomposition technique used in large-scale convex programming. The proposed method is based on a column generation technique defining a sequence of primal linear programming maximization problems. Associated with each problem one defines a weighted potential function which is minimized using a variant of the projective algorithm. When a point close to the minimum of the potential function is reached, a corresponding point in the dual space is constructed, which is close to the analytic center of a polytope containing the solution set of the nondifferentiable optimization problem. An admissible cut of the polytope, corresponding to a new supporting hyperplane of the epigraph of the function to minimize, is then generated at this approximate analytic center. In the primal space this new cut translates into a new column for the associated linear programming problem. The algorithm has performed well on a set of convex nondifferentiable programming problems.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by INFORMS in its journal Management Science.
Volume (Year): 38 (1992)
Issue (Month): 2 (February)
projective algorithm; interior point method; cutting plane; decomposition; nondifferentiable optimization;
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Dulce Rosas & Jordi Castro & Lídia Montero, 2009. "Using ACCPM in a simplicial decomposition algorithm for the traffic assignment problem," Computational Optimization and Applications, Springer, vol. 44(2), pages 289-313, November.
- Laurent Drouet & Alain Haurie & Francesco Moresino & Jean-Philippe Vial & Marc Vielle & Laurent Viguier, 2008. "An oracle based method to compute a coupled equilibrium in a model of international climate policy," Computational Management Science, Springer, vol. 5(1), pages 119-140, February.
- Benno Bueeler & Socrates Kypreos, . "Multiregional Markal-Macro: Introduction of CO Certificate Trade and Solution Concepts," Computing in Economics and Finance 1996 _011, Society for Computational Economics.
- Haurie, A., 1995. "Time scale decomposition in production planning for unreliable flexible manufacturing systems," European Journal of Operational Research, Elsevier, vol. 82(2), pages 339-358, April.
- Gondzio, J. & Sarkissian, R. & Vial, J.-P., 1997. "Using an interior point method for the master problem in a decomposition approach," European Journal of Operational Research, Elsevier, vol. 101(3), pages 577-587, September.
- Csaba Fábián & Olga Papp & Krisztián Eretnek, 2013. "Implementing the simplex method as a cutting-plane method, with a view to regularization," Computational Optimization and Applications, Springer, vol. 56(2), pages 343-368, October.
- Klose, Andreas & Gortz, Simon, 2007. "A branch-and-price algorithm for the capacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1109-1125, June.
- Rustem, Berc & Becker, Robin G. & Marty, Wolfgang, 2000. "Robust min-max portfolio strategies for rival forecast and risk scenarios," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1591-1621, October.
- Klose, Andreas, 2000. "A Lagrangean relax-and-cut approach for the two-stage capacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 126(2), pages 408-421, October.
- Gondzio, Jacek & González-Brevis, Pablo & Munari, Pedro, 2013. "New developments in the primal–dual column generation technique," European Journal of Operational Research, Elsevier, vol. 224(1), pages 41-51.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mirko Janc).
If references are entirely missing, you can add them using this form.