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Session TB10 - Avancées dans la programmation non linéaire dégénérée / Advances in Degenerate Nonlinear Programming

Day Tuesday, May 05, 2009
Room Dutailier International
President Dominique Orban

Presentations

01h30 PM-
01h55 PM
An L1 Elastic Interior-Point Method for MPCCs
  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.


01h55 PM-
02h20 PM
An Interior-Penalty Method for Mathematical Programs with Vanishing Constraints
  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.


02h20 PM-
02h45 PM
A Root-Finding Approach for Sparse Recovery and Approximation
  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.


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