Stephan Dempe This paper contributes to a deeper understanding of the link between a now conventional framework in hierarchical optimization spread under the name of the optimistic bilevel problem and its initial more dicult formulation that we call here the original optimistic bilevel optimization problem. It follows from this research that, although the process of deriving necessary … Read more
The paper is concerned with the optimistic formulation of a bilevel optimization problem with multiobjective lower-level problem. Considering the scalarization approach for the multiobjective program, we transform our problem into a scalar-objective optimization problem with inequality constraints by means of the well-known optimal value reformulation. Completely detailed rst-order necessary optimality conditions are then derived in … Read more
In 1997, Macal and Hurter have found that adding a constraint to the lower level problem, which is not active at the computed global optimal solution, can destroy global optimality. In this paper this property is reconsidered and it is shown that this solution remains locally optimal under inner semicontinuity of the original solution set … Read more
In this paper we formulate the fuzzy bilevel programming problem and describe one possible approach for formulating a crisp optimization problem being attached to it. Due to the nature of fuzzy bilevel programming this is a crisp bilevel programming problem. We compare our approach with one using multicriterial optimization and show, that both approaches are … Read more
In this paper a special step control problem is considered. The formulation of the problem uses a parameter to control the switching point. By using Taylor’s increment methods first and second order optimality conditions (in the sense of Pontryagin’s maximum principle) will be derived. Citation Preprint 2005-1, Department of Mathematics and Computer Science, Technical University … Read more
Linear programming problems with fuzzy coefficients in the objective function are considered. Emphasis is on the dependence of the optimal solution from linear perturbations of the membership functions of the objective function coefficients as well as on the computation of a robust solution of the fuzzy linear problem if the membership functions are not surely … Read more