Nonlinear Programming Formulations of Chance-Constraints

2/21/19 | 4:15pm | E51-335
Reception to follow.


 

 

 

 

Andreas Wächter

Associate Professor of Industrial Engineering and Management Sciences 
Northwestern University 


Abstract: We discuss a new approximation of chance constraints that results in differentiable functions which can be integrated in nonlinear optimization problems and solved with standard nonlinear programming techniques. For problems with joint chance constraints, our formulation can be used to develop a new trust-region sequential quadratic programming algorithm with provable convergence guarantees.

Our formulation is based on sample average approximation and considers a set of random realizations of the constraints. Often, a mixed-integer programming formulation is used in this setting to select which of the resulting constraints should be enforced to achieve the desired probability of constraint satisfaction. However, this approach typically results in large computation times, due to the implicit enumeration performed by the branch-and-bound algorithm. Instead, we propose a compact reformulation that combines all constraint scenarios in a single smooth constraint. This is achieved by means of a smoothed cumulative distribution function for the random constraint values. We will present theoretical convergence results, and numerical experiments for the solution of DC optimal power flow problems with joint chance constraints showcase the efficiency of this approach.

This is work in collaboration with Alejandra Pena-Ordieres at Northwestern University; James Luedtke and Line Roald at the University of Wisconsin-Madison; and Dan Molzahn at Georgia Tech.

Bio: Andreas Wächter is an Associate Professor in the Department of Industrial Engineering and Management Sciences at Northwestern University.  He obtained his master's degree in Mathematics at the University of Cologne, Germany, in 1997, and this Ph.D. in Chemical Engineering at Carnegie Mellon University in 2002.  Before joining Northwestern University in 2011, he was a Research Staff Member in the Department of Mathematical Sciences at IBM Research in Yorktown Heights, NY.  His research interests include the design, analysis, implementation and application of numerical algorithms for nonlinear continuous and mixed-integer optimization.  He is a recipient of the 2011 Wilkinson Prize for Numerical Software and the 2009 Informs Computing Society Prize for his work on the open-source optimization package Ipopt.

Event Time: 

2019 - 16:15