def projected_gradient(self, x0, g=None, active_set=None, qval=None, **kwargs):
"""
Perform a sequence of projected gradient steps starting from x0.
If the actual gradient at x is known, it should be passed using the
`g` keyword.
If the active set at x0 is known, it should be passed using the
`active_set` keyword.
If the value of the quadratic objective at x0 is known, it should
be passed using the `qval` keyword.
Return (x,(lower,upper)) where x is an updated iterate that satisfies
a sufficient decrease condition or at which the active set, given by
(lower,upper), settled down.
"""
maxiter = kwargs.get('maxiter', 10)
qp = self.qp
if g is None:
g = self.qp.grad(x0)
if qval is None:
qval = self.qp.obj(x0)
if active_set is None:
active_set = self.get_active_set(x0)
lower, upper = active_set
print 'Entering projected_gradient'
print ' qval=', qval, 'lower=', lower, ', upper=', upper
x = x0.copy()
settled_down = False
sufficient_decrease = False
best_decrease = 0
iter = 0
while not settled_down and not sufficient_decrease and \
iter < maxiter:
iter += 1
qOld = qval
# TODO: Use appropriate initial steplength.
(x, qval) = self.projected_linesearch(x, g, -g, qval)
# Check decrease in objective.
decrease = qOld - qval
if decrease <= self.pgrad_reltol * best_decrease:
sufficient_decrease = True
best_decrease = max(best_decrease, decrease)
# Check active set at updated iterate.
lowerTrial, upperTrial = self.get_active_set(x)
if identical(lower,lowerTrial) and identical(upper,upperTrial):
settled_down = True
lower, upper = lowerTrial, upperTrial
print ' qval=', qval, 'lower=', lower, ', upper=', upper
print ' settled=', repr(settled_down), ', decrease=', repr(sufficient_decrease)
return (x, (lower, upper))
def check_feasible(self, x):
"""
Safety function. Check that x is feasible with respect to the
bound constraints.
"""
Px = self.project(x)
if not identical(x,Px):
raise InfeasibleError, 'Received infeasible point.'
return None
def check_feasible(self, x):
"""
Safety function. Check that x is feasible with respect to the
bound constraints.
"""
Px = self.project(x)
if not identical(x, Px):
raise InfeasibleError, 'Received infeasible point.'
return None
def projected_gradient(self,
x0,
g=None,
active_set=None,
qval=None,
**kwargs):
"""
Perform a sequence of projected gradient steps starting from x0.
If the actual gradient at x is known, it should be passed using the
`g` keyword.
If the active set at x0 is known, it should be passed using the
`active_set` keyword.
If the value of the quadratic objective at x0 is known, it should
be passed using the `qval` keyword.
Return (x,(lower,upper)) where x is an updated iterate that satisfies
a sufficient decrease condition or at which the active set, given by
(lower,upper), settled down.
"""
maxiter = kwargs.get('maxiter', 10)
qp = self.qp
if g is None:
g = self.qp.grad(x0)
if qval is None:
qval = self.qp.obj(x0)
if active_set is None:
active_set = self.get_active_set(x0)
lower, upper = active_set
print 'Entering projected_gradient'
print ' qval=', qval, 'lower=', lower, ', upper=', upper
x = x0.copy()
settled_down = False
sufficient_decrease = False
best_decrease = 0
iter = 0
while not settled_down and not sufficient_decrease and \
iter < maxiter:
iter += 1
qOld = qval
# TODO: Use appropriate initial steplength.
(x, qval) = self.projected_linesearch(x, g, -g, qval)
# Check decrease in objective.
decrease = qOld - qval
if decrease <= self.pgrad_reltol * best_decrease:
sufficient_decrease = True
best_decrease = max(best_decrease, decrease)
# Check active set at updated iterate.
lowerTrial, upperTrial = self.get_active_set(x)
if identical(lower, lowerTrial) and identical(upper, upperTrial):
settled_down = True
lower, upper = lowerTrial, upperTrial
print ' qval=', qval, 'lower=', lower, ', upper=', upper
print ' settled=', repr(settled_down), ', decrease=', repr(
sufficient_decrease)
return (x, (lower, upper))
