An extension of the -type underestimation to linear parametric Hessian matrices

作者：Hladik Milan^*

来源：Journal of Global Optimization, 2016, 64(2): 217-231.

DOI：10.1007/s10898-015-0304-5

• Global optimization
• Interval computation
• Convex relaxation

The classical 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.

• 出版日期2016-2