Strong Wolfe Condition On Curvature
The Wolfe conditions, however, can result in a value for the step length that is not close to a minimizer of . If we modify the curvature condition to the following,
- iia)
then i) and iia) together form the so-called strong Wolfe conditions, and force to lie close to a critical point of .
The principal reason for imposing the Wolfe conditions in an optimization algorithm where is to ensure convergence of the gradient to zero. In particular, if the cosine of the angle between and the gradient,
is bounded away from zero and the i) and ii) hold, then .
An additional motivation, in the case of a quasi-Newton method is that if, where the matrix is updated by the BFGS or DFP formula, then if is positive definite ii) implies is also positive definite.
Read more about this topic: Wolfe Conditions
Famous quotes containing the words strong, wolfe and/or condition:
“Manuel showed her his open hand: “Look at this finger, how meager it seems, and this one even weaker, and this other one no stronger, and this one all by himself and on his own.”
Then he made a fist: “But now, is it strong enough, big enough, solid enough? It seems so doesn’t it?””
—Jacques Roumain (1907–1945)
“Frankly, these days, without a theory to go with it, I can’t see a painting.”
—Tom Wolfe (b. 1931)
“The sovereign being is burdened with a servitude that crushes him and the condition of free men is deliberate servility.”
—Georges Bataille (1897–1962)