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Zbl 1198.90347
Eichfelder, Gabriele
Multiobjective bilevel optimization. (English)
[J] Math. Program. 123, No. 2 (A), 419-449 (2010). ISSN 0025-5610; ISSN 1436-4646/e

This paper deals with nonlinear non-convex multi-objective bi-level optimization problems which are discussed using an optimistic approach. The author aims to obtain a good approximation of the feasible set of the upper level function by expressing it as the set of minimal solutions of a multi-objective optimization problem. To solve this problem he applies the scalarization approach of {\it A. Pascoletti} and {\it P. Serafini} [J. Optimization Theory Appl. 42, 499--524 (1984; Zbl 0505.90072)]. \par For generating the approximation mentioned above, the author uses sensitivity results for controlling the parameters of the corresponding scalarization problem adaptively. This sensitivity results are used again for solving the upper level problem in an iterative process. Thus, not only one minimal solution but an approximation of the whole efficient set of the multi-objective bilevel optimization problem is determined. \par The proposed numerical method (without convexity assumptions) demands twice continuously differentiable functions and appropriate solvers for determining global solutions of the scalar problems. \par Finally, an academic example and a topological problem arising in an application are solved with an algorithm designed for the case of a bi-criteria lower and upper level problem and a one-dimensional upper level variable.
[Francisco Guerra Vazquez (Puebla)]

MSC 2000:: *90C29 Multi-objective programming, etc.
90C31 Sensitivity, etc.
90C59 Approximation methods and heuristics

Keywords: multicriteria optimization; vector optimization; sensitivity; bilevel optimization; two-level optimization

Citations: Zbl 0505.90072

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