Bilevel convex programming models

Abstract

Bilevel convex models are studied after being cast into a parametric programming form. This form has a lexicographic inner-outer structure where the optimal value of the outer model is optimized on the set of optimal solutions of the inner model. Optimal solutions are characterized using a Lagrangian saddle-point approach and a marginal value formula is given for the outer model. These are used to formulate a general method for finding an optimal solution by input optimization.

Keywords:

• parameter
• bilevel convex programmes
• global and local optimum
• saddle point
• lower semicontinuity
• optimal value function
• marginal value formula

2000 Mathematics Subject Classifications:

• 90C25
• 90C31

Acknowledgement

The authors are indebted to the referee for his cogent remarks.