def __init__(self, nlp, **kwargs):
self.nlp = nlp
# Temporary error message as the class does not yet support
# range constraints
if nlp.nrangeC > 0:
msg = 'Range inequality constraints are not supported.'
raise ValueError, msg
# Analyze NLP to add slack variables to the formulation
# Ordering of the slacks in 'x' is assumed to be the order shown here
self.nx = nlp.n
self.nsLL = nlp.nlowerC
self.nsUU = nlp.nupperC
# self.nsLR = nlp.nrangeC
# self.nsUR = nlp.nrangeC
self.ns = nlp.nlowerC + nlp.nupperC + 2*nlp.nrangeC
self.n = self.nx + self.ns
self.m = nlp.m
# Copy initial data from NLP given new problem definition
# Initialize slack variables to zero
self.x0 = numpy.zeros(self.n,'d')
self.x0[:self.nx] = nlp.x0
self.pi0 = nlp.pi0.copy()
# Create Hessian approximation by default
self.approxHess = kwargs.get('approxHess',True)
if self.approxHess:
# LBFGS is currently the only option
self.Hessapp = LBFGS(self.n)
# Extend bound arrays to include slack variables
self.Lvar = numpy.zeros(self.n,'d')
self.Lvar[:self.nx] = nlp.Lvar
self.Uvar = nlp.Infinity*numpy.ones(self.n,'d')
self.Uvar[:self.nx] = nlp.Uvar
# Bring in bound arrays for constraints and lists of constraint types
self.Lcon = nlp.Lcon
self.Ucon = nlp.Ucon
self.lowerC = nlp.lowerC
self.upperC = nlp.upperC
# self.rangeC = nlp.rangeC
self.equalC = nlp.equalC
def store(self, new_s, new_y):
# Simply swap s and y.
LBFGS.store(self, new_y, new_s)
class AugmentedLagrangian(NLPModel):
'''
This class is a reformulation of an NLP, used to compute the
augmented Lagrangian function, gradient, and approximate Hessian in a
method-of-multipliers optimization routine. Slack variables are introduced
for inequality constraints and a function that computes the gradient
projected on to variable bounds is included.
Matrix-free NLP models are accomodated with the help of a Hessian
approximation which can be updated and restarted via calls to methods in
this class.
'''
def __init__(self, nlp, **kwargs):
self.nlp = nlp
# Temporary error message as the class does not yet support
# range constraints
if nlp.nrangeC > 0:
msg = 'Range inequality constraints are not supported.'
raise ValueError, msg
# Analyze NLP to add slack variables to the formulation
# Ordering of the slacks in 'x' is assumed to be the order shown here
self.nx = nlp.n
self.nsLL = nlp.nlowerC
self.nsUU = nlp.nupperC
# self.nsLR = nlp.nrangeC
# self.nsUR = nlp.nrangeC
self.ns = nlp.nlowerC + nlp.nupperC + 2*nlp.nrangeC
self.n = self.nx + self.ns
self.m = nlp.m
# Copy initial data from NLP given new problem definition
# Initialize slack variables to zero
self.x0 = numpy.zeros(self.n,'d')
self.x0[:self.nx] = nlp.x0
self.pi0 = nlp.pi0.copy()
# Create Hessian approximation by default
self.approxHess = kwargs.get('approxHess',True)
if self.approxHess:
# LBFGS is currently the only option
self.Hessapp = LBFGS(self.n)
# Extend bound arrays to include slack variables
self.Lvar = numpy.zeros(self.n,'d')
self.Lvar[:self.nx] = nlp.Lvar
self.Uvar = nlp.Infinity*numpy.ones(self.n,'d')
self.Uvar[:self.nx] = nlp.Uvar
# Bring in bound arrays for constraints and lists of constraint types
self.Lcon = nlp.Lcon
self.Ucon = nlp.Ucon
self.lowerC = nlp.lowerC
self.upperC = nlp.upperC
# self.rangeC = nlp.rangeC
self.equalC = nlp.equalC
# end def
# Evaluate infeasibility measure (used in both objective and gradient)
def get_infeas(self, x, **kwargs):
nx = self.nx
nsLL_ind = nx + self.nsLL
nsUU_ind = nsLL_ind + self.nsUU
# nsLR_ind = nsUU_ind + self.nsLR
# nsUR_ind = nsLR_ind + self.nsUR
convals = self.nlp.cons(x[:nx])
convals[self.lowerC] -= x[nx:nsLL_ind] + self.Lcon[self.lowerC]
convals[self.upperC] += x[nsLL_ind:nsUU_ind] - self.Ucon[self.upperC]
convals[self.equalC] -= self.Lcon[self.equalC]
# convals[self.rangeC] += x[nsLR_ind:nsUR_ind] - x[nsUU_ind:nsLR_ind]
return convals
# end def
# Evaluate augmented Lagrangian function
def obj(self, x, pi, rho, **kwargs):
nx = self.nx
nsLL_ind = nx + self.nsLL
nsUU_ind = nsLL_ind + self.nsUU
# nsLR_ind = nsUU_ind + self.nsLR
# nsUR_ind = nsLR_ind + self.nsUR
alfunc = self.nlp.obj(x[:nx])
convals = self.get_infeas(x)
alfunc += numpy.dot(pi,convals)
alfunc += 0.5*rho*numpy.sum(convals**2)
return alfunc
# end def
# Evaluate augmented Lagrangian gradient
def grad(self, x, pi, rho, **kwargs):
nlp = self.nlp
nx = self.nx
nsLL_ind = nx + self.nsLL
nsUU_ind = nsLL_ind + self.nsUU
# nsLR_ind = nsUU_ind + self.nsLR
# nsUR_ind = nsLR_ind + self.nsUR
algrad = numpy.zeros(self.n,'d')
algrad[:nx] = nlp.grad(x[:nx])
convals = self.get_infeas(x)
vec = pi + rho*convals
if isinstance(nlp, MFModel):
algrad[:nx] += nlp.jtprod(x[:nx],vec)
else:
algrad[:nx] += rho*numpy.dot(nlp.jac(x[:nx]).transpose(),vec)
# end if
algrad[nx:nsLL_ind] = -pi[nlp.lowerC] - rho*convals[nlp.lowerC]
algrad[nsLL_ind:nsUU_ind] = pi[nlp.upperC] + rho*convals[nlp.upperC]
# **Range constraint slacks here**
return algrad
# end def
def project_gradient(self, x, g, **kwargs):
'''
Project the provided gradient on to the bound-constrained space and
return the result. This is a helper function for determining
optimality conditions of the original NLP.
'''
p = x - g
med = numpy.maximum(numpy.minimum(p,self.Uvar),self.Lvar)
q = x - med
return q
def hprod(self, x, pi, rho, v, **kwargs):
'''
Compute the Hessian-vector produce of the Hessian of the augmented
Lagrangian with arbitrary vector v. Both exact and approximate
Hessians are supported.
'''
nlp = self.nlp
nx = self.nx
w = numpy.zeros(self.n,'d')
# Non-slack variables
if self.approxHess:
# Approximate Hessian
w = self.Hessapp.matvec(v)
else:
# Exact Hessian
# Note: the code in this block has yet to be properly tested
convals = self.get_infeas(x)
w[:nx] = nlp.hprod(x[:nx],pi,v[:nx],**kwargs)
for i in range(self.m):
w[:nx] += rho*convals[i]*nlp.hiprod(i,x[:nx],v[:nx])
# end for
if isinstance(nlp, MFModel):
w[:nx] += rho*nlp.jtprod(x[:nx],nlp.jprod(x[:nx],v[:nx]))
w[:nx] += rho*nlp.jprod(x[:nx],v[:nx])
w[nx:] += rho*nlp.jtprod(x[:nx],v[nx:])
else:
J = nlp.jac
w[:nx] += rho*numpy.dot(J.transpose(),numpy.dot(J,v[:nx]))
w[:nx] += rho*numpy.dot(J,v[:nx])
w[nx:] += rho*numpy.dot(J.transpose(),v[nx:])
# end if
# Slack variables
w[nx:] += rho*v[nx:]
# end if
return w
def hupdate(self, new_s=None, new_y=None):
if self.approxHess and new_s is not None and new_y is not None:
self.Hessapp.store(new_s,new_y)
return
def hrestart(self):
if self.approxHess:
self.Hessapp.restart()
return
def __init__(self, n, npairs=5, **kwargs):
LBFGS.__init__(self, n, npairs, **kwargs)