Discrete Interval Adjoints in Unconstrained Global Optimization

Deussen, Jens; Naumann, Uwe

doi:10.1007/978-3-030-21803-4_8

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2020

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Cited by 1 publication

(2 citation statements)

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“…The general idea of b&b algorithms [21] used for global optimization problems as given in ( 3) is to remove all parts of the domain that cannot contain a global minimum. The implementation used for this case study is a variation of the one presented in [17] implementing Theorem 1. The user needs to specify at least one separator.…”

Section: Case Studymentioning

confidence: 99%

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Subdomain Separability in Global Optimization

Deussen¹,

Naumann²

2020

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We propose a generalization of separability in the context of global optimization. Our results apply to objective functions implemented as differentiable computer programs. They are presented in the context of a simple branch and bound method. The often significant search space reduction can be expected to yield an acceleration of any global optimization method. We show how to utilize interval derivatives calculated by adjoint algorithmic differentiation to examine the monotonicity of the objective with respect to so called structural separators and how to verify the latter automatically.

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Section: Case Studymentioning

confidence: 99%

“…In [16] we discussed significance analysis in the context of neural networks. Deterministic global optimization through a check for first-order optimality is described in [17]. In the following we show how to use interval adjoints for a monotonicity check of structural separators and for the verification of these separators.…”

Section: Introductionmentioning

confidence: 99%