Generalized Pc 1 -functions and Their Application to Bilevel Programming Problems
نویسنده
چکیده
In this paper we consider bilevel programming problems in which the lower level problem is not assumed to have unique optimal solutions for all values of the parameter. Using common approaches to treat such problems, a generally discontinuous function is to be minimized. This leads to the deenition of a new class of functions, so-called generalized PC 1-functions which are composed by a nite number of continuously diierentiable functions. We investigate them using the radial-directional derivative and a radial subdiierential and give criteria for optimality for minimizing such a function. These results are then applied to linear bilevel programming problems.
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