Foundations of Bilevel Programming, Vol. 61 Book

1	Introduction	1
2	Applications	7
2.1	Stackelberg games	7
2.2	Optimal chemical equilibria	11
2.3	Environmental economics	12
2.4	Discrimination between sets	15
3	Linear Bilevel Problems	21
3.1	The model and one example	21
3.2	The geometric nature of linear bilevel programming	24
3.3	Existence of optimal solutions	27
3.4	Relations to other MP problems	31
3.5	Optimality conditions	36
3.6	Solution algorithms	47
4	Parametric Optimization	61
4.1	Optimality conditions	62
4.2	Upper semicontinuity of the solution set mapping	64
4.3	Piecewise continuously differentiable functions	70
4.4	Properties of optimal solutions	75
4.5	Properties of the optimal value function	88
5	Optimality Conditions	119
5.1	Optimality concepts	121
5.2	Optimality conditions based on strong stability	129
5.3	The contingent cone to the feasible set	135
5.4	Regularity	145
5.5	Optimality conditions using the KKT reformulation	149
5.6	The approach via the lower level optimal value function	155
5.7	Generalized PC[superscript 1] functions	158
6	Solution Algorithms	193
6.1	A descent algorithm	194
6.2	A bundle algorithm	200
6.3	Penalty methods	209
6.4	A trust region method	211
6.5	Smoothing methods	215
7	Nonunique Lower Level Solution	217
7.1	Approximation of desired solutions	218
7.2	Stability of bilevel problems	226
7.3	Special perturbations	230
8	Discrete Bilevel Problems	255
8.1	Two introductory examples	255
8.2	Cutting plane algorithm	258
8.3	Inner approximation	264
8.4	Knapsack lower level problems	266
	References	283
	Notations	303
	Index	305