Cedric Josz - Efficient Computational Methods for Large-Scale Systems with Applications to Power Systems and Machine Learning

Description

Abstract: Computation is the key for the design and operation of intelligent, efficient, reliable and resilient societal systems. In many real-world systems (e.g., smart grids, intelligent transportation systems, smart cities), one is faced with issues of nonlinearity and scalability. We thus propose numerical algorithms for nonconvex optimization that work on a large-scale and come equipped with global convergence guarantees. One approach consists in convex relaxations that provide converging lower bounds toward the optimal value, thanks to deep results in algebraic geometry. In that regard, we present the first successful application of sum-of-squares to a large-scale industrial problem since they were introduced two decades ago. Global solutions to the optimal power flow problem are computed on instances of the European transmission grid with several thousand nodes. Another approach we consider consists in local search algorithms that can be guaranteed to converge by proving the absence of spurious local solutions - and indeed this is a flourishing area of machine learning. We present a general theory for making global guarantees on nonconvex and nonsmooth optimization. We discuss applications in data science and particularly deep neural networks. Bio: Cédric Josz is currently a postdoctoral scholar at the University of California, Berkeley in the department of Electrical Engineering and Computer Sciences under the supervision of Professor Sojoudi and Professor Lavaei. Previously, he was a postdoctoral scholar under the supervision of Jean Bernard Lasserre at the LAAS CNRS Toulouse, France. His PhD in applied mathematics was completed in 2016 at the University of Paris VI under the supervision of Jean Charles Gilbert. It was in collaboration with French transmission system operator and the French Institute for Research in Computer Science and Automation. He was awarded the best paper award of 2016 from Springer Optimization Letters for his work on polynomial optimization. He was also a finalist of the competition for best PhD thesis of 2017 organized by French Agency for Mathematics in Interaction with Industry and Society.