Skip to content

Parametric global optimisation for bilevel programming

by Nuno P. Faísca, Vivek Dua, Berç Rustem, Pedro M. Saraiva, Efstratios N. Pistikopoulos
Journal of Global Optimization ()
Get full text at journal


We propose a global optimisation approach for the solution of various classes of bilevel programming problems (BLPP) based on recently developed para- metric programming algorithms. We first describe how we can recast and solve the inner (follower’s) problem of the bilevel formulation as a multi-parametric program- ming problem, with parameters being the (unknown) variables of the outer (leader’s) problem. By inserting the obtained rational reaction sets in the upper level prob- lem the overall problem is transformed into a set of independent quadratic, linear or mixed integer linear programming problems, which can be solved to global optimality. In particular, we solve bilevel quadratic and bilevel mixed integer linear problems, with or without right-hand-side uncertainty. A number of examples are presented to illustrate the steps and details of the proposed global optimisation strategy.

Cite this document (BETA)

Authors on Mendeley

Readership Statistics

24 Readers on Mendeley
by Discipline
42% Engineering
17% Computer Science
13% Business, Management and Accounting
by Academic Status
33% Student > Ph. D. Student
21% Professor > Associate Professor
13% Researcher
by Country
4% United Kingdom
4% China
4% Norway

Sign up today - FREE

Mendeley saves you time finding and organizing research. Learn more

  • All your research in one place
  • Add and import papers easily
  • Access it anywhere, anytime

Start using Mendeley in seconds!

Sign up & Download

Already have an account? Sign in