Frank-Wolfe Algorithm - Objective Approximation Previous Next
Initial trial solution:
We begin the first iteration by developing a "linear approximation" for  near this trial solution. This is done by evaluating the partial derivatives at (0, 0):
so this approximation is .
Maximizing  subject to the original constraints yields the solution
  with . However since (2, 1) is not near
(0, 0) the approximation may not be a good one at (2, 1). [Note that  is well under .] Rather than just accepting (2, 1) as the next trial solution , let us check the line segment between (0, 0) and (2, 1) and choose the
  with the largest .