Two-phase model algorithm with global convergence for nonlinear programming
Journal of Optimization Theory and Applications
A New Projection Method for Variational Inequality Problems
SIAM Journal on Control and Optimization
Inexact-restoration algorithm for constrained optimization
Journal of Optimization Theory and Applications
Modified Wilson'S Method for Nonlinear Programswith Nonunique Multipliers
Mathematics of Operations Research
On the Accurate Identification of Active Constraints
SIAM Journal on Optimization
Convergence Properties of the BFGS Algoritm
SIAM Journal on Optimization
Large-Scale Active-Set Box-Constrained Optimization Method with Spectral Projected Gradients
Computational Optimization and Applications
A Trust-Region Method for Nonlinear Bilevel Programming: Algorithm and Computational Experience
Computational Optimization and Applications
Local Convergence of SQP Methods for Mathematical Programs with Equilibrium Constraints
SIAM Journal on Optimization
Practical Bilevel Optimization: Algorithms and Applications (Nonconvex Optimization and Its Applications)
Inexact Restoration for Runge-Kutta Discretization of Optimal Control Problems
SIAM Journal on Numerical Analysis
International Journal of Approximate Reasoning
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We present a new algorithm for solving bilevel programming problems without reformulating them as single-level nonlinear programming problems. This strategy allows one to take profit of the structure of the lower level optimization problems without using non-differentiable methods. The algorithm is based on the inexact-restoration technique. Under some assumptions on the problem we prove global convergence to feasible points that satisfy the approximate gradient projection (AGP) optimality condition. Computational experiments are presented that encourage the use of this method for general bilevel problems.