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Structural properties of Pareto fronts: the occurrence of dents in classical and parametric multiobjective optimization problems. (English) Zbl 07271603
Junge, Oliver (ed.) et al., Advances in dynamics, optimization and computation. A volume dedicated to Michael Dellnitz on the occasion of his 60th birthday. Cham: Springer (ISBN 978-3-030-51263-7/hbk; 978-3-030-51264-4/ebook). Studies in Systems, Decision and Control 304, 315-336 (2020).
Summary: This contribution deals with the occurrence of “dents” in Pareto fronts of continuous and adequately smooth multiobjective optimization problems. After giving a formal definition of this notion, a system of equations is derived that characterizes points on the boundary of the dent. This can be used to obtain information about the structure of the Pareto front without computing the entire Pareto set. Furthermore, the evolution of dents in parametric multiobjective optimization problems is studied using results from bifurcation theory. Theory and computations are illustrated by several examples, whose construction is described as well.
For the entire collection see [Zbl 1445.37003].
MSC:
65K Numerical methods for mathematical programming, optimization and variational techniques
90 Operations research, mathematical programming
Software:
AUTO2000; HomCont; NBI
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