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Interactive bundle-based method for nondifferentiable multiobjective optimization: NIMBUS. (English) Zbl 0855.90114
Summary: NIMBUS, an interactive method for nondifferentiable multiobjective optimization problems, is described. The algorithm is based on the classification of objective functions. At each iteration, a decision maker is asked to classify the objective functions into up to five different classes: those to be improved, those to be improved till some aspiration level, those to be accepted as they are, those to be impaired till some bound, and those allowed to change freely.
According to the classification, a new (multiobjective) optimization problem is formed, which is solved by an MPB (Multiobjective Proximal Bundle) method. The MPB method is a generalization of Kiwiel’s proximal bundle approach for nondifferentiable single objective optimization into the multiobjective case. The multiple objective functions are treated individually without employing any scalarization. The method is capable of handling several nonconvex locally Lipschitz continuous objective functions subject to nonlinear (possibly nondifferentiable) constraints.
Finally, numerical experiments with two academic test problems are reported. The aim is to briefly demonstrate how the method works.

MSC:
90C29 Multi-objective and goal programming
49J52 Nonsmooth analysis
Software:
NIMBUS; NSOLIB
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References:
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