We are concerned with weak Stackelberg problems such as those considered in [19], [23] and [25]. Based on a method due to Molodtsov, we present new results to approximate such problems by sequences of strong Stackelberg problems. Results related to convergence of marginal functions and approximate solutions are given. The case of data perturbations is Mso considered.
We consider a bilevel optimization problem where the upper level is a scalar optimization problem and the lower level is a vector optimization problem. For the lower level, we deal with weakly efficient solutions. We approach our problem using a suitable penalty function which vanishes over the weakly efficient solutions of the lower-level vector optimization problem and which is nonnegative over its feasible set. Then, we use an exterior penalty method
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