I am pursuing a postdoc under the supervision of Somayeh Sojoudi and Javad Lavaei at the University of California, Berkeley, in the department of Electrical Engineering and Computer Sciences. My research mainly focuses on solving nonconvex optimization problems to global optimality, either via convex relaxations or local search algorithms. Applications include computing optimal power flows in high-voltage transmission grids and handling outliers in recommender systems (e.g. the netflix problem). Some other interests are the stability of power grids after a contingency, as well as the recovery of a sparse signal from few measurements (e.g. super resolution).
Contact: cedric.josz at gmail dot com or Etcheverry Hall, 2521 Hearst Ave, Berkeley, CA 94709
Interests: optimization, machine learning, power systems, control theory
PhD Thesis: Application of polynomial optimization to electricity transmission networks, defended on July 13th 2016 (slides).
Tutorial: Convexification techniques and hierarchies, American Control Conference, June 2018.
Video: Application of complex polynomial optimization for optimal power flow, Banff International Research Station, March 2017.
Preprints and Publications: [arXiv]
C. Josz, D. K. Molzahn, M. Tacchi, S. Sojoudi, Transient stability analysis of power systems via occupation measures, IEEE PES Innovative Smart Grid Technologies Conference, Washington D.C., February 2018.
C. Josz, Y. Ouyang, R. Y. Zhang, J. Lavaei, S. Sojoudi, A theory on the absence of spurious solutions for nonconvex and nonsmooth optimization, NeurIPS, Montreal, December 2018, [poster] [video].
R. Y. Zhang, C. Josz, S. Sojoudi, J. Lavaei, How much restricted isometry is needed in nonconvex matrix recovery?, NeurIPS spotlight, Montreal, December 2018, [video].
R. Y. Zhang, C. Josz, S. Sojoudi, Conic optimization theory: convexification techniques and numerical algorithms, American Control Conference 2018, Milwaukee, June 2018.
C. Josz, D. K. Molzahn, Lasserre hierarchy for large scale polynomial optimization in real and complex variables, SIAM Journal on Optimization, January 2018 (preprint).
C. Josz, J. B. Lasserre, B. Mourrain, Sparse polynomial interpolation: compressed sensing, super resolution, or Prony?, August 2017.
C. Josz, Counterexample to global convergence of DSOS and SDSOS hierarchies, July 2017.
C. Josz, On the relationship between real and complex linear systems, May 2017.
C. Josz, Algorithm for optimization and interpolation based on hyponormality, March 2017.
J. C. Gilbert, C. Josz, Plea for a semidefinite optimization solver in complex numbers, March 2017.
D. K. Molzahn, C. Josz, I. A. Hiskens, Moment relaxations of optimal power flow problems: beyond the convex hull, Institute of Electrical and Electronics Engineers, Global Conference on Signal and Information Processing, Washington D.C., December 2016 (preprint).
C. Josz, S. Fliscounakis, J. Maeght, and P. Panciatici, AC power flow data in MATPOWER and QCQP format: iTesla, RTE snapshots, and PEGASE, arXiv, March 2016.
D. K. Molzahn, C. Josz, I. A. Hiskens, P. Panciatici, Computational analysis of sparsity exploiting moment relaxations of the OPF problem, 19th Power Systems Computation Conference, Genoa, June 2016 (preprint).
D. K. Molzahn, C. Josz, I. A. Hiskens, P. Panciatici, A Laplacian-based approach for finding near globally optimal solutions to OPF problems, Institute of Electrical and Electronics Engineers, Transactions on Power Systems, April 2016 (preprint).
D. K. Molzahn, C. Josz, I. A. Hiskens, P. Panciatici, Solution of optimal power flow problems using moment relaxations augmented with objective function penalization, 54th Conference on Decision and Control, Osaka, December 2015 (preprint).
C. Josz, D. Henrion, Strong duality in Lasserre's hierarchy for polynomial optimization, Springer, Optimization Letters, February 2015.
C. Josz, J. Maeght, P. Panciatici, and J. C. Gilbert, Application of the moment-SOS approach to global optimization of the OPF problem, Institute of Electrical and Electronics Engineers, Transactions on Power Systems, May 2014, (preprint).
C. Josz, S. Fliscounakis, J. Maeght, and P. Panciatici, Power flow data for European high-voltage transmission network: 89, 1354, 2869, and 9241-bus PEGASE systems, MATPOWER 5.1, March 2015.
C. Josz, Analysis of the paper "Zero duality gap in optimal power flow problem" by J. Lavaei and S. Low, internship report, RTE, 2012.
C. Josz, Convex approximation of power generation for medium-term hydro dispatch scheduling, internship report, Ecole Polytechnique Montréal, supervision by Michel Gendreau, 2011.
Winner of the 2016 Best Paper Award in Springer Optimization Letters (for the paper Strong duality in Lasserre’s hierarchy for polynomial optimization).
Finalist of the competition for best PhD thesis of 2017 organized by AMIES (French Agency for Mathematics in Interaction with Industry and Society).