### Bilevel programs with extremal value function: global optimality.

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We describe an interior point algorithm for convex quadratic problem with a strict complementarity constraints. We show that under some assumptions the approach requires a total of $O\left(\sqrt{n}L\right)$ number of iterations, where $L$ is the input size of the problem. The algorithm generates a sequence of problems, each of which is approximately solved by Newton’s method.

We describe an interior point algorithm for convex quadratic problem with a strict complementarity constraints. We show that under some assumptions the approach requires a total of $O\left(\sqrt{n}L\right)$ number of iterations, where is the input size of the problem. The algorithm generates a sequence of problems, each of which is approximately solved by Newton's method.

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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