Abstract
This chapter presents techniques for dealing with constrained global optimization of real valued functions defined on smooth manifolds, subject to equality constraints. Functional constraints must satisfy certain smoothness conditions, not excluding simultaneous restrictions of different types, being the effect of dimensional reduction proportional to the number of equality restrictions. The problems under study do not need to restrict cost functions to be differentiable or even continuous, and the optimization task is done so as to keep candidate points inside corresponding submanifolds, evolving therein along the optimization process. The techniques may be employed together with an extensive family of already tested evolutionary methods and, after introducing the fundamental ideas, selected examples will demonstrate the effectiveness of the presented methods.
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Aguiar e Oliveira Junior, H. (2016). Constrained Global Optimization on Manifolds. In: Evolutionary Global Optimization, Manifolds and Applications. Studies in Systems, Decision and Control, vol 43. Springer, Cham. https://doi.org/10.1007/978-3-319-26467-7_4
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DOI: https://doi.org/10.1007/978-3-319-26467-7_4
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