Daniel Bienstock


342 S.W. Mudd
Mailcode 4712

Tel(212) 854-3407
Fax(212) 854-8103

Daniel Bienstock’s current research focuses on two complementary topics. He is studying problems related to analysis and operations of power transmission networks, including analysis of the vulnerabilities of electrical power grids, a topic of increasing relevance to society and also one of fascinating mathematical complexity which he explores in a book recently published by SIAM. 

Research Interests

All aspects of optimization, in particular discrete, nonlinear and robust optimization, from the perspective of theory, computational experimentation and application, vulnerability analysis of power grids.

The mathematics of power grids is nonlinear and nonconvex, as well as stochastic.  A second recent thrust focuses on mixed-integer nonlinear programming problems and more generally polynomial optimization problems. 

The physics of power networks is nonlinear and subject to noise due to ambient conditions, ill-defined control actions (including human actions), and imprecise device operation.  This subjects mathematical algorithms to complex forms of data uncertainty. Yet engineering practice demands precise answers and actions. An interesting topic is the verification of near-feasibility or infeasibility of candidate solutions to algebraic systems. 

Bienstock received a BA in mathematics from Brandeis University in 1982 and a PhD in operations research from Massachusetts Institute of Technology in 1985He is a fellow of INFORMS and was a plenary speaker at the 2005 SIAM Optimization Conference and a semi-plenary speaker at ISMP 2006.  He has received a Presidential Young Investigator Award and an IBM Faculty Partnership Award. He joined the faculty of Columbia Engineering in 1989 after working in combinatorics and optimization research at Bellcore. 


  • Professor of applied mathematics and applied physics, Columbia University, 2008-
  • Full professor of industrial engineering and operations research, Columbia University, 1995-
  • Associate professor of industrial engineering and operations research, Columbia University, 1989-1990 (tenured 1991)
  • Assistant professor of industrial engineering and operations research, Columbia University, 1989–1990
  • Scientist, combinatorics and optimization research, Bellcore, 1986-1989
  • Assistant professor, Graduate School of Industrial Administration, Carnegie Mellon University, 1985-1986


  • SIAM
  • IEEE


  • INFORMS Fellow, 2014
  •  Plenary speaker, 2005 SIAM Optimization Conference, semi-plenary speaker, ISMP 2006
  •  Presidential Young Investigator Award, 1990   


  • D. Bienstock and G. Munoz, LP formulations for mixed-integer polynomial optimization problems (20014), arXiv 1501.00288. 
  • D. Bienstock and A. Michalka, Polynomial solvability of variants of the trust-region subproblem, Proc. 25th ACM-SIAM Symp. on Discrete Algorithms (2014), 380-390.
  • D. Bienstock, M. Chertkov and S. Harnett, Chance-constrained DC-OPF, SIAM Review 56 (2014), 461 – 495.
  • D. Bienstock, Optimal control of cascading power grid failures, Proc. 2011 IEEE PES Meeting, Proc. 2011 joint CDC-IEEE meeting.
  • D. Bienstock, The N – k Problem in Power Grids: New Models, Formulations and Numerical Experiments, SIAM J. Optimization 20 (2010) 1052-6234.
  • D. Bienstock, Electrical Transmission System Cascades and Vulnerability: An Operations Research Viewpoint,  ISBN 978-1-611974-15-7. SIAM-MOS Series on Optimization (2015).
  • D. Bienstock, T. Kim, S. Harnett and S. Wright,  Analyzing Vulnerability of Power Systems with Continuous Optimization Formulations, IEEE Trans. Network Science and Eng. 3 (2016), 132 – 146.
  • D. Bienstock, J. Blanchet and J. Li, Stochastic models and control for electrical power line temperature, Energy Systems 7 2016) 173 -- 192. 
  • D. Bienstock, A note on polynomial solvability of the CDT problem, SIAM J. Optimization 26 (2016) 486–496.
  • A. Bernstein, D. Bienstock, D. Hay, M. Uzunoglu and G. Zussman, Sensitivity Analysis of Power Grid Vulnerability to Large-Scale Cascading Failures, ACM Performance Evaluation Review, Special issue of papers from ACM Greenmetrics’12, Vol. 40, No. 3 (Dec. 2012), pp. 33 -37.