Verifying the Solution from a Nonlinear Solver: A Case Study: Comment
评论了McCullough和Vinod关于通过Hessian矩阵条件数验证非线性优化估计有效性的建议，指出问题并非如他们所述那样直接，并以Ron Shachar和Barry Nalebuff的解为例说明其结论有误。
In a recent article in this journal, B. D. McCullough and H. D. Vinod (2003; hereafter MV) argue that checking the condition number of the Hessian should be a standard part of checking the validity of any estimates obtained via nonlinear optimization. While we think that looking at the condition number of the Hessian is a good idea, we argue that the issue is not as straightforward as claimed by MV. To illustrate our point, we show that MV reached the wrong conclusion about the validity of the Ron Shachar and Barry Nalebuff (1999) solution. In Sections I–III of their article, MV note that it is possible for a well-coded log-likelihood program to declare convergence when some of the parameters are not identified for the given data set. Furthermore, MV make several important recommendations including that researchers check that