WORKSHOP - OPTIMIZATION AND DATA ASSIMILATION

**Toulouse, January 13th-15th 2016 **

CERFACS, Toulouse, January 13th-15th 2016

**Programme and organization:**

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Here are the slides for talks given at the workshop

Y. Nesterov | Structural Optimization: New perspectives for increasing efficiency of numerical schemes |

C. Sun | On a spectral structured matrix problem |

Z. Zhang | A subspace decomposition framework for nonlinear optimization |

S. Gürol | Numerical solution of the time-parallelized weak-constraint 4DVAR |

L.N. Vicente | Recent Progress on Derivative-Free Trust-Region Methods |

E. Riccietti | A regularization trust-region approach for ill-posed nonlinear systems |

C. Royer | Second-order convergence in direct-search methods |

P. Sakov | Notes on the EnKF and its application in ocean forecasting |

O. Burdakov | A reduction of cardinality to complementarity in sparse optimization |

S. Wright | Data Assimilation from the Big Data Perspective |

F. Lenti | Lp-regularization in variational data assimilation |

In this workshop, we want to address the challenge of solving nonlinear large scale and structured problems on high performance computers. We focus on large scale nonlinear and non-quadratic optimization problems that arise for instance in the domain of numerical simulation or prediction in physical systems. Available algorithms from the literature, or from well-known libraries, are often less than satisfactory for tackling these kinds of problem. Most of them do not allow execution on massively parallel computers while, at the same time, taking into account the problem structure. We consider that successful algorithms should exploit problem features such as, for example, partial separability that can be seen as a sort of nonlinear counterpart to sparsity in a matrix. Another important feature that might be desirable is the existence of some subspace on which the optimization problem can be approximately solved either yielding a reasonable solution or a new subspace on which the optimization can be further continued. At first sight, these methods could be seen as natural extensions of linear algebra methods (such as multigrid, domain decomposition or projection methods) to nonlinear problem. This view is partially true and really

shows the connection of these techniques with highly efficient linear algebra methods that are the main focus of the other events of this CIMI semester. However the extension of these ideas to nonlinear problems is rather complex, because it must include a focus on the following difficulties, that are often encountered in practice: global convergence of the methods, noisy problems, problems without derivatives, stopping criteria for inner and outer iterations. In that respect, we believe that this satellite event will be important for people involved in high performance computing, linear algebra, and numerical optimization.

Confirmed invited speakers are currently Yurii Nesterov (Louvain University, Belgium), Pavel Sakov (Bureau of Meteorology, Australia), Luis Nunes Vicente (University of Coimbra, Portugal), Stephen Wright (University of Wisconsin, USA) and Oleg Burdakov (Linkoping University,

Sweden).

For further information please contact Serge Gratton (serge.gratton@enseeiht.fr) and Ehouarn Simon (ehouarn.simon@enseeiht.fr).