Derivative evaluation and computational experience with large bilevel mathematical programs

A bilevel program is a mathematical program involving functions defined implicitly as solutions to another mathematical program. We discuss a method for extracting derivative information on the implicit function, which is especially efficient when the lower-level problem has simple bounds on the variables and/or many inactive constraints. Computational experience on problems with up to 230 variables and 30 constraints is presented.Computational support from Robert Bivins and Myron Stein is gratefully acknowledged. We have also appreciated comments from Jon Bard and an anonymous referee. This work was supported in part by the US Department of Energy through the Los Alamos National Laboratory.