However, there are examples where all choices of
still result in step lengths that satisfy
the Wolfe conditions, e.g. consider a a line search on
where the tangent line at 0,
,
cuts through the graph leaving a strict local minimum below the line.
Therefore, any value of
close to 1 still cuts of this local
minimum. And, any value of
will not eliminate the points with a
positive slope that follows the local minimum. (See Figure 1.)
The graph was generated by the following matlab program.
y=[1 .9 .8 .7 .3 -.1 -.5 -.1 .3 .7]; x=[0:9]; xx = 0:.25:9; yy = spline(x,y,xx); plot(x,y,'o',xx,yy) slope=-.1; y=slope*x+1; hold on plot(x,y,'x:')