1 research outputs found
An Efficient Inexact Newton-CG Algorithm for the Smallest Enclosing Ball Problem of Large Dimensions
In this paper, we consider the problem of computing the smallest enclosing
ball (SEB) of a set of balls in where the product is
large. We first approximate the non-differentiable SEB problem by its
log-exponential aggregation function and then propose a computationally
efficient inexact Newton-CG algorithm for the smoothing approximation problem
by exploiting its special (approximate) sparsity structure. The key difference
between the proposed inexact Newton-CG algorithm and the classical Newton-CG
algorithm is that the gradient and the Hessian-vector product are inexactly
computed in the proposed algorithm, which makes it capable of solving the
large-scale SEB problem. We give an adaptive criterion of inexactly computing
the gradient/Hessian and establish global convergence of the proposed
algorithm. We illustrate the efficiency of the proposed algorithm by using the
classical Newton-CG algorithm as well as the algorithm from [Zhou. {et al.} in
Comput. Opt. \& Appl. 30, 147--160 (2005)] as benchmarks.Comment: 25 pages, 1 figure, Journal of the Operations Research Society of
China, 201