def primal_dual_hess(self, x, z, **kwargs):
"""
Assemble the "primal-dual" Hessian matrix of the merit function
at (x,z):
[ H + 2 X^{-1} Z I ]
[ I Z^{-1} X ].
"""
mu = kwargs.get('mu', self.mu)
nlp = self.nlp ; nx = nlp.n ; nz = self.nz
Lvar = nlp.Lvar ; Uvar = nlp.Uvar
lB = nlp.lowerB ; uB = nlp.upperB ; rB = nlp.rangeB
nlB = nlp.nlowerB ; nuB = nlp.nupperB ; nrB = nlp.nrangeB
rlB = self.rlB ; ruB = self.ruB ; rrB = self.rrB
# Segment s and z for conciseness.
slB = x[lB] - Lvar[lB] ; zlB = z[:nlB]
suB = Uvar[uB] - x[uB] ; zuB = z[nlB:nlB+nuB]
srlB = x[rB] - Lvar[rB] ; zrlB = z[nlB+nuB:nlB+nuB+nrB]
sruB = Uvar[rB] - x[rB] ; zruB = z[nlB+nuB+nrB:]
H = sp(nrow=nx+nz, ncol=nx+nz,
sizeHint=self.nlp.nnzh+3*nz, symmetric=True)
# Leading block: H + 2 * mu X^{-2}.
H[:nx,:nx] = self.nlp.hess(x, self.nlp.pi0)
H.addAt(2 * zlB / slB, lB, lB)
H.addAt(2 * zuB / suB, uB, uB)
H.addAt(2 * zrlB/srlB, rB, rB)
H.addAt(2 * zruB/sruB, rB, rB)
# Bottom left block: identity-ish.
n1 = nx + rlB ; H.put( 1, n1, lB)
n2 = nx + ruB ; H.put(-1, n2, uB)
n3 = nx + rrB ; H.put( 1, n3, rB)
n4 = nx + nrB + rrB ; H.put(-1, n4, rB)
# Bottom right block: mu * Z^{-2}.
H.put(slB / zlB, n1, n1)
H.put(suB / zuB, n2, n2)
H.put(srlB/zrlB, n3, n3)
H.put(sruB/zruB, n4, n4)
return H
def _hess_template(self, **kwargs):
"""
Assemble the part of the modified Hessian matrix of the primal-dual
merit function that is iteration independent.
"""
nlp = self.nlp ; nx = nlp.n ; nz = self.nz
Lvar = nlp.Lvar ; Uvar = nlp.Uvar
lB = nlp.lowerB ; uB = nlp.upperB ; rB = nlp.rangeB
nlB = nlp.nlowerB ; rlB = self.rlB
nuB = nlp.nupperB ; ruB = self.ruB
nrB = nlp.nrangeB ; rrB = self.rrB
B = sp(nrow=nx+nz, ncol=nx+nz,
sizeHint=self.nlp.nnzh+3*nz, symmetric=True)
# Bottom left block: identity-ish.
n1 = nx + rlB ; B.put( 1, n1, lB)
n2 = nx + ruB ; B.put(-1, n2, uB)
n3 = nx + rrB ; B.put( 1, n3, rB)
n4 = nx + nrB + rrB ; B.put(-1, n4, rB)
return B
def _hess_template(self, **kwargs):
"""
Assemble the part of the modified Hessian matrix of the primal-dual
merit function that is iteration independent.
"""
nlp = self.nlp
nx = nlp.n
nz = self.nz
Lvar = nlp.Lvar
Uvar = nlp.Uvar
lB = nlp.lowerB
uB = nlp.upperB
rB = nlp.rangeB
nlB = nlp.nlowerB
rlB = self.rlB
nuB = nlp.nupperB
ruB = self.ruB
nrB = nlp.nrangeB
rrB = self.rrB
B = sp(nrow=nx + nz,
ncol=nx + nz,
sizeHint=self.nlp.nnzh + 3 * nz,
symmetric=True)
# Bottom left block: identity-ish.
n1 = nx + rlB
B.put(1, n1, lB)
n2 = nx + ruB
B.put(-1, n2, uB)
n3 = nx + rrB
B.put(1, n3, rB)
n4 = nx + nrB + rrB
B.put(-1, n4, rB)
return B
def primal_dual_hess(self, x, z, **kwargs):
"""
Assemble the "primal-dual" Hessian matrix of the merit function
at (x,z):
[ H + 2 X^{-1} Z I ]
[ I Z^{-1} X ].
"""
mu = kwargs.get('mu', self.mu)
nlp = self.nlp
nx = nlp.n
nz = self.nz
Lvar = nlp.Lvar
Uvar = nlp.Uvar
lB = nlp.lowerB
uB = nlp.upperB
rB = nlp.rangeB
nlB = nlp.nlowerB
nuB = nlp.nupperB
nrB = nlp.nrangeB
rlB = self.rlB
ruB = self.ruB
rrB = self.rrB
# Segment s and z for conciseness.
slB = x[lB] - Lvar[lB]
zlB = z[:nlB]
suB = Uvar[uB] - x[uB]
zuB = z[nlB:nlB + nuB]
srlB = x[rB] - Lvar[rB]
zrlB = z[nlB + nuB:nlB + nuB + nrB]
sruB = Uvar[rB] - x[rB]
zruB = z[nlB + nuB + nrB:]
H = sp(nrow=nx + nz,
ncol=nx + nz,
sizeHint=self.nlp.nnzh + 3 * nz,
symmetric=True)
# Leading block: H + 2 * mu X^{-2}.
H[:nx, :nx] = self.nlp.hess(x, self.nlp.pi0)
H.addAt(2 * zlB / slB, lB, lB)
H.addAt(2 * zuB / suB, uB, uB)
H.addAt(2 * zrlB / srlB, rB, rB)
H.addAt(2 * zruB / sruB, rB, rB)
# Bottom left block: identity-ish.
n1 = nx + rlB
H.put(1, n1, lB)
n2 = nx + ruB
H.put(-1, n2, uB)
n3 = nx + rrB
H.put(1, n3, rB)
n4 = nx + nrB + rrB
H.put(-1, n4, rB)
# Bottom right block: mu * Z^{-2}.
H.put(slB / zlB, n1, n1)
H.put(suB / zuB, n2, n2)
H.put(srlB / zrlB, n3, n3)
H.put(sruB / zruB, n4, n4)
return H