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Section: New Results
Nonsmooth optimisation and applications
Semidefinite programming and combinatorial optimization
Participant : Jérôme Malick.
We have worked with Frederic Roupin (Prof. at Paris XIII) and Nathan Krislock (Assistant Prof. at North Illinois University, USA) on the use of semidefinite programming to solve combinatorial optimization problems to optimality. Nathan was the guest of the team during 2 months (June/July).
We have worked on a generic semidefinite-based solver for solve binary quadratic optimization problems. Using the generality of the bounds proposed in [54] . Our article is in revision in ACM Transaction of Mathematical Software. Our solver and our data sets are available online at http://lipn.univ-paris13.fr/BiqCrunch/ .
Specializing the method of the k-cluster problem, we have proposed in [51] an algorithm able to solve exactly k-cluster instances of size 160. In practice, our method works particularly fine on the most difficult instances (with a large number of vertices, small density and small k).
Stochastic optimization for electricity production
Participant : Jérôme Malick.
Everyday, electricity generation companies submit a generation schedule to the grid operator for the coming day; computing an optimal schedule is called the unit-commitment problem. In collaboration with W. van Ackooij from EDF, we have proposed in [44] a two-stage formulation of unit-commitment to better include the impact of renewable energies. We present a primal-dual decomposition approach to tackle large-scale instances of these two-stage problems, wherein both the first and second stage problems are full unit-commitment problems. We provide an analysis of the theoretical properties of the algorithm, as well as computational experiments showing the interest of the approach for real-life large-scale unit-commitment instances.