I am an assistant professor in Industrial Engineering and Operations Research at Columbia University. My research deals with continuous optimization and applied algebraic geometry. My PhD students are Xiaopeng Li, Lexiao Lai (former), and I have a postdoc Wenqing Ouyang.
Contact: cj2638@columbia.edu, office 308, S. W. Mudd Building, 500 W 120th St, New York, NY 10027-6623.
Sufficient conditions for instability of the subgradient method with constant step size, L. Lai, SIAM Journal on Optimization, January 2024.
Convergence of the momentum method for semialgebraic functions with locally Lipschitz gradients, L. Lai, X. Li, SIAM Journal on Optimization, November 2023.
Global stability of first-order methods for coercive tame functions, L. Lai, Mathematical Programming, October 2023.
Certifying the absence of spurious local minima at infinity, X. Li, SIAM Journal on Optimization, July 2023.
Global convergence of the gradient method for functions definable in o-minimal structures, Mathematical Programming, February 2023.
Lyapunov stability of the subgradient method with constant step size, L. Lai, Mathematical Programming, February 2023.
Nonsmooth rank-one matrix factorization landscape, L. Lai, Optimization Letters, November 2021.
Verifying Global Optimality of Candidate Solutions to Polynomial Optimization Problems using a Determinant Relaxation Hierarchy, S. Xu, R. Ma, D. K. Molzahn, H. Hijazi, IEEE Conference on Decision and Control, Austin, December 2021.
Absence of spurious local trajectories in time-varying optimization: a control-theoretic perspective, S. Fattahi, R. Mohammadi, J. Lavaei, S. Sojoudi, IEEE Conference on Control Technology and Applications, Montreal, August 2020.
A survey on conic relaxations of optimal power flow problem, F. Zohrizadeh, M. Jin, R. Madani, J. Lavaei, S. Sojoudi, European Journal of Operational Research, January 2020.
Sparse polynomial interpolation: compressed sensing, super resolution, or Prony?, J. B. Lasserre, B. Mourrain, Advances in Computational Mathematics, February 2019.
Transient stability analysis of power systems via occupation measures, D. K. Molzahn, M. Tacchi, S. Sojoudi, IEEE PES Innovative Smart Grid Technologies Conference, Washington D.C., February 2018.
A theory on the absence of spurious solutions for nonconvex and nonsmooth optimization, Y. Ouyang, R. Y. Zhang, J. Lavaei, S. Sojoudi, NeurIPS, Montreal, December 2018, [poster] [video].
How much restricted isometry is needed in nonconvex matrix recovery?, R. Y. Zhang, S. Sojoudi, J. Lavaei, NeurIPS spotlight, Montreal, December 2018, [video].
Conic optimization theory: convexification techniques and numerical algorithms, R. Y. Zhang, S. Sojoudi, American Control Conference 2018, Milwaukee, June 2018.
Lasserre hierarchy for large scale polynomial optimization in real and complex variables, D. K. Molzahn, SIAM Journal on Optimization, January 2018 (preprint).
Counterexample to global convergence of DSOS and SDSOS hierarchies, July 2017.
On the relationship between real and complex linear systems, May 2017.
Algorithm for optimization and interpolation based on hyponormality, March 2017.
Plea for a semidefinite optimization solver in complex numbers, J. C. Gilbert, March 2017.
Moment relaxations of optimal power flow problems: beyond the convex hull, D. K. Molzahn, I. A. Hiskens, Institute of Electrical and Electronics Engineers, Global Conference on Signal and Information Processing, Washington D.C., December 2016 (preprint).
AC power flow data in MATPOWER and QCQP format: iTesla, RTE snapshots, and PEGASE, S. Fliscounakis, J. Maeght, and P. Panciatici, arXiv, March 2016.
Computational analysis of sparsity exploiting moment relaxations of the OPF problem, D. K. Molzahn, I. A. Hiskens, P. Panciatici, 19th Power Systems Computation Conference, Genoa, June 2016 (preprint).
A Laplacian-based approach for finding near globally optimal solutions to OPF problems, D. K. Molzahn, I. A. Hiskens, P. Panciatici, Institute of Electrical and Electronics Engineers, Transactions on Power Systems, April 2016 (preprint).
Solution of optimal power flow problems using moment relaxations augmented with objective function penalization, D. K. Molzahn, I. A. Hiskens, P. Panciatici, 54th Conference on Decision and Control, Osaka, December 2015 (preprint).
Strong duality in Lasserre's hierarchy for polynomial optimization, D. Henrion, Springer, Optimization Letters, February 2015.
Application of the moment-SOS approach to global optimization of the OPF problem, J. Maeght, P. Panciatici, and J. C. Gilbert, Institute of Electrical and Electronics Engineers, Transactions on Power Systems, May 2014, (preprint).
Power flow data for European high-voltage transmission network: 89, 1354, 2869, and 9241-bus PEGASE systems, S. Fliscounakis, J. Maeght, and P. Panciatici, MATPOWER 5.1, March 2015.
Analysis of the paper "Zero duality gap in optimal power flow problem" by J. Lavaei and S. Low, internship report, RTE, 2012.
Convex approximation of power generation for medium-term hydro dispatch scheduling, internship report, Ecole Polytechnique Montréal, supervision by Michel Gendreau, 2011.