Fast computation of Lipschitz constants on hyperrectangles using sparse codelists

摘要: Abstract We propose and compare methods for the efficient calculation of Lipschitz constants differentiable functions on hyperrectangular sets. Two new approaches are presented here that inspired by techniques Hessian spectral bounds αBB, a method Professor Christodoulos A. Floudas proposed as young researcher continuously refined over his entire career. to existing ones with respect two features, their computational cost, tightness resulting constants. The algorithms designed require fewer operations than ones. Not surprisingly, they result in fairly conservative show, however, this conservatism can be mitigated considerably incorporating structural information. More specifically, all considered use codelists extended first order derivatives. Extended involve sparse intermediate gradients, since early codelist lines depend very few variables construction (for any nontrivial function, not just special cases). This sparsity used improve cost from theoretical point view corroborate results large number experiments involving several hundred sample random claim one is an attractive option many sets (such global branch bound optimization), it less computationally expensive provides similar