Séance TB10 - Avancées dans la programmation non linéaire dégénérée / Advances in Degenerate Nonlinear Programming
Jour mardi, le 05 mai 2009 Salle Dutailier International Président Dominique Orban
Présentations
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13h30- 13h55 |
An L1 Elastic Interior-Point Method for MPCCs |
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Zoumana Coulibaly, École Polytechnique de Montréal, Mathematics and Industrial Engeneering/GERAD, C.P. 6079, Succ. Centre-Ville, Montréal, Québec, Canada, H3C 3A7 Dominique Orban, GERAD et École Polytechnique de Montréal, Mathématiques et génie industriel, C.P. 6079, Succ. Centre-ville, Montréal, Québec, Canada, H3C 3A7 We propose an interior-point algorithm based on an elastic formulation of the L1-penalty merit function for mathematical programs with complementarity constraints. The method naturally converges to a strongly stationary point or delivers a certificate of degeneracy without recourse to second-order intermediate solutions. Numerical results on a standard test set illustrate the efficiency and robustness of the approach. |
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13h55- 14h20 |
An Interior-Penalty Method for Mathematical Programs with Vanishing Constraints |
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Dominique Orban, GERAD et École Polytechnique de Montréal, Mathématiques et génie industriel, C.P. 6079, Succ. Centre-ville, Montréal, Québec, Canada, H3C 3A7 Pierre-Rémi Curatolo, GEARD, École Polytechnique de Montréal, Mathematics and Industrial Engeneering, C.P. 6079, Succ. Centre-Ville, Montréal, Québec, Canada, H3C 3A7 MPVCs are degenerate nonlinear programs that model topology and structural optimization problems. They resemble problems with complementarity constraints yet different sets of qualification conditions are used to formulate necessary optimality conditions. We extend of a mixed interior/exterior elastic penalty method to MPVCs. Global and fast local convergence are established. We illustrate our algorithm on instances of structural problems. |
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14h20- 14h45 |
A Root-Finding Approach for Sparse Recovery and Approximation |
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Ewout van den Berg, University of British Columbia, Computer Science, 201-2366 Main Mall, Vancouver, BC, Canada, V6T 1Z4 Michael P. Friedlander, University of British Columbia, Computer Science, Vancouver, British Columbia, Canada, V6T 1Z4 Theoretical results in compressed sensing justify the use of l1-regularization to obtain sparse least-squares solutions. We present an algorithm that can efficiently solve a wide range of sparse recovery and approximation problems, including sign-constrained and joint-sparsity problems. We explore possible generalizations and compare its performance to existing solvers. |