Integer and combinatorial optimization
Integer and combinatorial optimization
Journal of Optimization Theory and Applications
The mixed integer linear bilevel programming problem
Operations Research
Generating linear and linear-quadratic bilevel programming problems
SIAM Journal on Scientific Computing
A new technique for generating quadratic programming test problems
Mathematical Programming: Series A and B
Generating quadratic bilevel programming test problems
ACM Transactions on Mathematical Software (TOMS)
On bilevel programming, part I: general nonlinear cases
Mathematical Programming: Series A and B
Interval analysis: theory and applications
Journal of Computational and Applied Mathematics - Special issue on numerical analysis in the 20th century vol. 1: approximation theory
Introduction to Linear Optimization
Introduction to Linear Optimization
Global Optimization of Nonlinear Bilevel Programming Problems
Journal of Global Optimization
Convexification and Global Optimization in Continuous And
Convexification and Global Optimization in Continuous And
Outer approximation algorithms for separable nonconvex mixed-integer nonlinear programs
Mathematical Programming: Series A and B
Interval methods for semi-infinite programs
Computational Optimization and Applications
A Trust-Region Method for Nonlinear Bilevel Programming: Algorithm and Computational Experience
Computational Optimization and Applications
Global solution of semi-infinite programs
Mathematical Programming: Series A and B
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
Practical Bilevel Optimization: Algorithms and Applications (Nonconvex Optimization and Its Applications)
A novel approach to Bilevel nonlinear programming
Journal of Global Optimization
The Adaptive Convexification Algorithm: A Feasible Point Method for Semi-Infinite Programming
SIAM Journal on Optimization
Relaxation-Based Bounds for Semi-Infinite Programs
SIAM Journal on Optimization
A review of recent advances in global optimization
Journal of Global Optimization
Towards global bilevel dynamic optimization
Journal of Global Optimization
Global solution of nonlinear mixed-integer bilevel programs
Journal of Global Optimization
A lifting method for generalized semi-infinite programs based on lower level Wolfe duality
Computational Optimization and Applications
Hi-index | 0.00 |
A bounding algorithm for the global solution of nonlinear bilevel programs involving nonconvex functions in both the inner and outer programs is presented. The algorithm is rigorous and terminates finitely to a point that satisfies 驴-optimality in the inner and outer programs. For the lower bounding problem, a relaxed program, containing the constraints of the inner and outer programs augmented by a parametric upper bound to the parametric optimal solution function of the inner program, is solved to global optimality. The optional upper bounding problem is based on probing the solution obtained by the lower bounding procedure. For the case that the inner program satisfies a constraint qualification, an algorithmic heuristic for tighter lower bounds is presented based on the KKT necessary conditions of the inner program. The algorithm is extended to include branching, which is not required for convergence but has potential advantages. Two branching heuristics are described and analyzed. Convergence proofs are provided and numerical results for original test problems and for literature examples are presented.