Paper Info
Title
An extension of the αBB-type underestimation to linear parametric Hessian matrices.
Abstract
The classical $$alpha hbox {BB}$$?BB method is a global optimization method the important step of which is to determine a convex underestimator of an objective function on an interval domain. Its particular point is to enclose the range of a Hessian matrix in an interval matrix. To have a tighter estimation of the Hessian matrices, we investigate a linear parametric form enclosure in this paper. One way to obtain this form is by using a slope extension of the Hessian entries. Numerical examples indicate that our approach can sometimes significantly reduce overestimation on the objective function. However, the slope extensions highly depend on a choice of the center of linearization. We compare some naive choices and also propose a heuristic one, which performs well in executed examples, but it seems there is no one global winner.
Year
Venue
Field
2016
J. Global Optimization
Hessian equation,Parametric equation,Mathematical optimization,Global optimization,Matrix (mathematics),Hessian matrix,Parametric statistics,Interval arithmetic,Linearization,Mathematics
DocType
Volume
Issue
Journal
64
2
Citations 
PageRank 
References 
0
0.34
13
Authors
1
Name
Order
Citations
PageRank
Milan Hladík126836.33