Stability of Regularized Bilevel Programming Problems

M. B. Lignola and Jacqueline Morgan
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M. B. Lignola: Università di Napoli “Federico II,”

Journal of Optimization Theory and Applications, 1997, vol. 93, issue 3, No 8, 575-596

Abstract: Abstract A bilevel programming problem S is considered. First, sufficient conditions of minimal character are given on the data of the problem in order to guarantee the lower semicontinuity of the marginal function of the upper level problem. Then, for ε>0, a regularized problem S(ε) is considered for which continuity of the regularized marginal function and convergence of the approximate value, as ε goes to zero, are obtained. Moreover, under perturbations on the data, convergence results for the perturbed marginal functions and the solutions to the problem S n(ε) are given for any ε>0.

Keywords: Bilevel programming problems; strong Stackelberg problems; marginal functions; epiconvergence; convergence of multi-functions; convergence of solutions; convergence of values (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (14)

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DOI: 10.1023/A:1022695113803

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