Sensitivity analysis of nonlinear programs and differentiability properties of metric projections
SIAM Journal on Control and Optimization
Proximity control in bundle methods for convex
Mathematical Programming: Series A and B
Directional differentiability of optimal solutions under Slater's condition
Mathematical Programming: Series A and B
A numerical approach to optimization problems with variational inequality constraints
Mathematical Programming: Series A and B
On bilevel programming, part I: general nonlinear cases
Mathematical Programming: Series A and B
Directional derivatives of the solution of a parametric nonlinear program
Mathematical Programming: Series A and B
On an algorithm solving two-level programming problems with nonunique lower level solutions
Computational Optimization and Applications
A Smoothing Method for a Mathematical Program with P-Matrix Linear Complementarity Constraints
Computational Optimization and Applications
Potential formal models for autonomic computing applications
Proceedings of the 11th International Conference on Computer Systems and Technologies and Workshop for PhD Students in Computing on International Conference on Computer Systems and Technologies
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In the paper, the question isinvestigated if a bundle algorithm can be usedto compute approximate solutions for bilevelprogramming problems where the lower leveloptimal solution is in general not uniquelydetermined. To give a positive answer to thisquestion, an appropriate regularizationapproach is used in the lower level. In thegeneral case, the resulting algorithm computesan approximate solution. If the problem provesto have strongly stable lower level solutionsfor all parameter values in a certainneighborhood of the stationary solutions of thebilevel problem, convergence to stationarysolutions can be shown.