On Tue, May 12, 2015 at 09:06:02AM -0400, Grey Gordon wrote:
> Is this an analytical gradient?

No, finite differences

> Perhaps it is incorrect.

It is correct. If I run steepest descent for 3 iterations then the fit 
rapidly improves.

> For minimization, its clear from this gradient where the direction of 
> steepest descent is.

For sure!

> So if it can’t use this information to get closer to a local minimum, 
> then I would think there is something wrong with the input or bizarre 
> about the function.

No, that isn't what I'm saying. This gradient works great even without 
any Hessian approximation. The problem is that SLSQP reports "positive 
directional derivative for linesearch" and gives up. It would be nice if 
SLSQP could start optimization from here, even though the starting 
values are not great.

> > On May 11, 2015, at 4:00 PM, Joshua N Pritikin <jpriti...@pobox.com> wrote:
> > 
> > During optimization, I have a problem that gets to a point where the 
> > gradient looks like this,
> > 
> > [0] gradient = t( matrix(c(    # 51x1
> > -31780.195562, -38508.674735, -50973.208738, -55408.084812, 
> > -66931.026056, -74286.656477, -80710.037658, -32059.100573, 
> > -40421.260358, -47351.363022, -56331.397546, -67570.244335, 
> > -71730.720066, -80617.938563, -30100.959330, -40235.309256, 
> > -47047.853982, -56263.225828, -67009.403836, -75987.083372, 
> > -84897.553874, -62848.356157, -210680.805240, -214470.061730, 
> > -234536.487353, -241645.958717, -262177.928304, -278085.836093, 
> > -286557.250051, -63655.124325, -214492.388535, -219036.315591, 
> > -224526.862707, -240634.971741, -248375.386046, -263267.566427, 
> > -289505.767031, -64899.664139, -213624.942908, -222084.527486, 
> > -223847.520561, -236782.323103, -258931.376366, -276562.312245, 
> > -304241.522192, -25035.332609, -25125.410641, -25003.755675, 
> > -4302.824452, -4986.836691, -3574.837605), byrow=TRUE, nrow=1, ncol=51))
> > 
> > This point is nowhere near the minimum. Is it significant that all the 
> > gradients are negative? Is that why SLSQP cannot determine a search 
> > direction? When this occurs, could SLSQP use the gradient as the search 
> > direction?

-- 
Joshua N. Pritikin
Department of Psychology
University of Virginia
485 McCormick Rd, Gilmer Hall Room 102
Charlottesville, VA 22904
http://people.virginia.edu/~jnp3bc

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