I am an assistant professor in Industrial Engineering and Operations Research at Columbia University. My research mainly focuses on designing tractable and guaranteed algorithms for non-convex optimization with application to power systems and data science. In more technical terms, I am interested in the interplay between conic optimization, algebraic geometry, and polynomial optimization. I am currently advising PhD student Lexiao Lai.
Contact: email@example.com, office 308, S. W. Mudd Building, 500 W 120th St, New York, NY 10027-6623.
Interests: optimization, power systems, data science.
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]
S. Fattahi , C. Josz , R. Mohammadi , J. Lavaei , S. Sojoudi, Absence of spurious local trajectories in time-varying optimization: a control-theoretic perspective, IEEE Conference on Control Technology and Applications (CCTA), Montreal, August 2020.
F. Zohrizadeh, C. Josz, M. Jin, R. Madani, J. Lavaei, S. Sojoudi, A survey on conic relaxations of optimal power flow problem, European Journal of Operational Research, January 2020.
C. Josz, J. B. Lasserre, B. Mourrain, Sparse polynomial interpolation: compressed sensing, super resolution, or Prony?, Advances in Computational Mathematics, February 2019.
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, 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).