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We are concerned with two-level optimization problems called strongweak
Stackelberg problems, generalizing the class of Stackelberg problems in the
strong and weak sense. In order to handle the fact that the considered two-level
optimization problems may fail to have a solution under mild assumptions, we
consider a regularization involving ε-approximate optimal solutions in the lower
level problems. We prove the existence of optimal solutions for such regularized
problems and present some approximation...
In this paper, which is an extension of [4],
we first show the existence of solutions to
a class of Min Sup problems with
linked constraints, which satisfy a certain property. Then, we apply our result to a class of weak nonlinear bilevel
problems. Furthermore, for such a class of bilevel problems, we
give a relationship with appropriate d.c. problems concerning the
existence of solutions.
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