Computational difficulties of bilevel linear programming
Operations Research
Some properties of the bilevel programming problem
Journal of Optimization Theory and Applications
A non-interior-point continuation method for linear complementarity problems
SIAM Journal on Matrix Analysis and Applications
Descent approaches for quadratic bilevel programming
Journal of Optimization Theory and Applications
Smoothing methods for convex inequalities and linear complementarity problems
Mathematical Programming: Series A and B
Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity
Mathematics of Operations Research
Global Optimization of Nonlinear Bilevel Programming Problems
Journal of Global Optimization
Genetic algorithm based on simplex method for solving linear-quadratic bilevel programming problem
Computers & Mathematics with Applications
Application of particle swarm optimization algorithm for solving bi-level linear programming problem
Computers & Mathematics with Applications
A neural network approach to multiobjective and multilevel programming problems
Computers & Mathematics with Applications
An approximate programming method based on the simplex method for bilevel programming problem
Computers & Mathematics with Applications
Bilevel model for production-distribution planning solved by using ant colony optimization
Computers and Operations Research
Practical Bilevel Optimization: Algorithms and Applications
Practical Bilevel Optimization: Algorithms and Applications
On bilevel multi-follower decision making: General framework and solutions
Information Sciences: an International Journal
A global optimization method for nonlinear bilevel programmingproblems
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
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Bilevel programming techniques deal with decision processes involving two decision makers with a hierarchical structure. In this paper, an augmented Lagrangian multiplier method is proposed to solve nonlinear bilevel programming (NBLP) problems. An NBLP problem is first transformed into a single level problem with complementary constraints by replacing the lower level problem with its Karush-Kuhn-Tucker optimality condition, which is sequentially smoothed by a Chen-Harker-Kanzow-Smale (CHKS) smoothing function. An augmented Lagrangian multiplier method is then applied to solve the smoothed nonlinear program to obtain an approximate optimal solution of the NBLP problem. The asymptotic properties of the augmented Lagrangian multiplier method are analyzed and the condition for solution optimality is derived. Numerical results showing viability of the approach are reported.