def solver(graph=None, update=False, full=False, data=None, SO=False):
"""Find the UE link flow
Parameters
----------
graph: graph object
update: if update==True: update link flows and link,path delays in graph
full: if full=True, also return x (link flows per OD pair)
data: (Aeq, beq, ffdelays, parameters, type) from get_data(graph)
"""
if data is None: data = get_data(graph)
Aeq, beq, ffdelays, pm, type = data
n = len(ffdelays)
p = Aeq.size[1]/n
A, b = spmatrix(-1.0, range(p*n), range(p*n)), matrix(0.0, (p*n,1))
if type == 'Polynomial':
if not SO: pm = pm * spdiag([1.0/(j+2) for j in range(pm.size[1])])
def F(x=None, z=None): return objective_poly(x, z, matrix([[ffdelays], [pm]]), p)
if type == 'Hyperbolic':
if SO:
def F(x=None, z=None): return objective_hyper_SO(x, z, matrix([[ffdelays-div(pm[:,0],pm[:,1])], [pm]]), p)
else:
def F(x=None, z=None): return objective_hyper(x, z, matrix([[ffdelays-div(pm[:,0],pm[:,1])], [pm]]), p)
dims = {'l': p*n, 'q': [], 's': []}
x = solvers.cp(F, G=A, h=b, A=Aeq, b=beq, kktsolver=get_kktsolver(A, dims, Aeq, F))['x']
linkflows = matrix(0.0, (n,1))
for k in range(p): linkflows += x[k*n:(k+1)*n]
if update:
logging.info('Update link flows, delays in Graph.'); graph.update_linkflows_linkdelays(linkflows)
logging.info('Update path delays in Graph.'); graph.update_pathdelays()
if full: return linkflows, x
return linkflows
def solver(graph=None, update=False, full=False, data=None, SO=False):
"""Find the UE link flow
Parameters
----------
graph: graph object
update: if update==True: update link flows and link,path delays in graph
full: if full=True, also return x (link flows per OD pair)
data: (Aeq, beq, ffdelays, parameters, type) from get_data(graph)
"""
if data is None: data = get_data(graph)
Aeq, beq, ffdelays, pm, type = data
n = len(ffdelays)
p = Aeq.size[1]/n
A, b = spmatrix(-1.0, range(p*n), range(p*n)), matrix(0.0, (p*n,1))
if type == 'Polynomial':
if not SO: pm = pm * spdiag([1.0/(j+2) for j in range(pm.size[1])])
def F(x=None, z=None): return objective_poly(x, z, matrix([[ffdelays], [pm]]), p)
if type == 'Hyperbolic':
if SO:
def F(x=None, z=None): return objective_hyper_SO(x, z, matrix([[ffdelays-div(pm[:,0],pm[:,1])], [pm]]), p)
else:
def F(x=None, z=None): return objective_hyper(x, z, matrix([[ffdelays-div(pm[:,0],pm[:,1])], [pm]]), p)
dims = {'l': p*n, 'q': [], 's': []}
x = solvers.cp(F, G=A, h=b, A=Aeq, b=beq, kktsolver=get_kktsolver(A, dims, Aeq, F))['x']
linkflows = matrix(0.0, (n,1))
for k in range(p): linkflows += x[k*n:(k+1)*n]
if update:
logging.info('Update link flows, delays in Graph.'); graph.update_linkflows_linkdelays(linkflows)
logging.info('Update path delays in Graph.'); graph.update_pathdelays()
if full: return linkflows, x
return linkflows
def feasible_pathflows(graph, l_obs, obs=None, update=False,
with_cell_paths=False, with_ODs=False, x_true=None, wp_trajs=None):
"""Attempts to find feasible pathflows given partial of full linkflows
Parameters:
----------
graph: Graph object
l_obs: observations of link flows
obs: indices of the observed links
update: if True, update path flows in graph
with_cell_paths: if True, include cell paths as constraints
with_ODs: if True, include ODs in the constraints if no with_cell_paths or in the objective if with_cell_paths
"""
assert with_cell_paths or with_ODs # we must have some measurements!
n = graph.numpaths
# route to links flow constraints
A, b = linkpath_incidence(graph), l_obs
if obs: A = A[obs,:] # trim matrix if we have partial observations
Aineq, bineq = spmatrix(-1.0, range(n), range(n)), matrix(0.0, (n,1)) # positive constraints
if not with_cell_paths: # if just with ODs flow measurements:
Aeq, beq = path_to_OD_simplex(graph) # route to OD flow constraints
else: # if we have cellpath flow measurements:
assert wp_trajs is not None
Aeq, beq = WP.simplex(graph, wp_trajs) # route to cellpath flow constraints
if with_ODs: # if we have ODs + cellpaths measurements
T, d = path_to_OD_simplex(graph) # route to OD flow constraints included in objective
A, b = matrix([A, T]), matrix([b, d]) # add the constraints to the objective
if x_true is not None:
err1 = np.linalg.norm(A * x_true - b, 1) / np.linalg.norm(b, 1)
err2 = np.linalg.norm(Aeq * x_true - beq) / np.linalg.norm(beq, 1)
assert err1 < TOL, 'Ax!=b'
assert err2 < TOL, 'Aeq x!=beq'
# construct objective for cvxopt.solvers.qp
Q, c = A.trans()*A, -A.trans()*b
#x = solvers.qp(Q + REG_EPS*spmatrix(1.0, range(n), range(n)), c, Aineq, bineq, Aeq, beq)['x']
# try with cvxopt.solvers.cp
def qp_objective(x=None, z=None):
if x is None: return 0, matrix(1.0, (n, 1))
f = 0.5 * x.trans()*Q*x + c.trans() * x
Df = (Q*x + c).trans()
if z is None: return f, Df
return f, Df, z[0]*Q
dims = {'l': n, 'q': [], 's': []}
x = solvers.cp(qp_objective, G=Aineq, h=bineq, A=Aeq, b=beq,
kktsolver=get_kktsolver(Aineq, dims, Aeq, qp_objective))['x']
if update:
logging.info('Update link flows, delays in Graph.'); graph.update_linkflows_linkdelays(P*x)
logging.info('Update path delays in Graph.'); graph.update_pathdelays()
logging.info('Update path flows in Graph object.'); graph.update_pathflows(x)
#import ipdb
#rank = 5
#if with_ODs == False:
# ipdb.set_trace()
return x, rn.rank(matrix([A, Aeq])), n
def _solve(self, solver=s.ECOS, ignore_dcp=False, verbose=False):
if not self.is_dcp():
if ignore_dcp:
print ("Problem does not follow DCP rules. "
"Solving a convex relaxation.")
else:
raise Exception("Problem does not follow DCP rules.")
objective,constr_map,dims = self.canonicalize()
var_offsets,x_length = self.variables(objective,
constr_map[s.EQ] + constr_map[s.INEQ])
c,obj_offset = self.constraints_matrix([objective], var_offsets, x_length,
self.dense_interface, self.dense_interface)
A,b = self.constraints_matrix(constr_map[s.EQ], var_offsets, x_length,
self.interface, self.dense_interface)
G,h = self.constraints_matrix(constr_map[s.INEQ], var_offsets, x_length,
self.interface, self.dense_interface)
# ECHU: get the nonlinear constraints
F = self.nonlinear_constraint_function(constr_map[s.NONLIN], var_offsets,
x_length)
# Save original cvxopt solver options.
old_options = cvxopt.solvers.options
# Silence cvxopt if verbose is False.
cvxopt.solvers.options['show_progress'] = verbose
# Always do one step of iterative refinement after solving KKT system.
cvxopt.solvers.options['refinement'] = 1
# Target cvxopt clp if nonlinear constraints exist
if constr_map[s.NONLIN]:
# Get custom kktsolver.
kktsolver = get_kktsolver(G, dims, A, F)
results = cvxopt.solvers.cpl(c.T,F,G,h,A=A,b=b,
dims=dims,kktsolver=kktsolver)
status = s.SOLVER_STATUS[s.CVXOPT][results['status']]
primal_val = results['primal objective']
# Target cvxopt solver if SDP or invalid for ECOS.
elif solver == s.CVXOPT or len(dims['s']) > 0 or min(G.size) == 0:
# Get custom kktsolver.
kktsolver = get_kktsolver(G, dims, A)
# Adjust tolerance to account for regularization.
cvxopt.solvers.options['feastol'] = 2*1e-6
results = cvxopt.solvers.conelp(c.T,G,h,A=A,b=b,
dims=dims,kktsolver=kktsolver)
status = s.SOLVER_STATUS[s.CVXOPT][results['status']]
primal_val = results['primal objective']
else: # If possible, target ECOS.
# ECHU: ecos interface has changed and no longer relies on CVXOPT
# as a result, we have to convert cvxopt data structures into
# numpy arrays
#
# ideally, CVXPY would no longer user CVXOPT, except when calling
# conelp
#
cnp, hnp, bnp = map(lambda x: np.fromiter(iter(x),dtype=np.double,count=len(x)), (c, h, b))
Gp,Gi,Gx = G.CCS
m,n1 = G.size
Ap,Ai,Ax = A.CCS
p,n2 = A.size
Gp, Gi, Ap, Ai = map(lambda x: np.fromiter(iter(x),dtype=np.int32,count=len(x)), (Gp,Gi,Ap,Ai))
Gx, Ax = map(lambda x: np.fromiter(iter(x),dtype=np.double,count=len(x)), (Gx, Ax))
Gsp = sp.csc_matrix((Gx,Gi,Gp),shape=(m,n1))
if p == 0:
Asp = None
bnp = None
else:
Asp = sp.csc_matrix((Ax,Ai,Ap),shape=(p,n2))
# ECHU: end conversion
results = ecos.solve(cnp,Gsp,hnp,dims,Asp,bnp,verbose=verbose)
status = s.SOLVER_STATUS[s.ECOS][results['info']['exitFlag']]
primal_val = results['info']['pcost']
# Restore original cvxopt solver options.
cvxopt.solvers.options = old_options
if status == s.SOLVED:
self.save_values(results['x'], sorted(var_offsets.keys()))
self.save_values(results['y'], constr_map[s.EQ])
if constr_map[s.NONLIN]:
self.save_values(results['zl'], constr_map[s.INEQ])
else:
self.save_values(results['z'], constr_map[s.INEQ])
return self.objective.value(primal_val - obj_offset[0])
else:
return status
def _cvxopt_solve(self, objective, constr_map, dims,
sorted_vars, var_offsets, x_length,
verbose):
"""Calls the CVXOPT conelp or cpl solver and returns the result.
Parameters
----------
objective: Expression
The canonicalized objective.
constr_map: dict
A dict of the canonicalized constraints.
dims: dict
A dict with information about the types of constraints.
sorted_vars: list
An ordered list of the problem variables.
var_offsets: dict
A dict mapping variable id to offset in the stacked variable x.
x_length: int
The height of x.
verbose: bool
Should the solver show output?
Returns
-------
tuple
(status, optimal objective, optimal x,
optimal equality constraint dual,
optimal inequality constraint dual)
"""
c, obj_offset = self._constr_matrix([objective], var_offsets, x_length,
self._CVXOPT_DENSE_INTF,
self._CVXOPT_DENSE_INTF)
# Convert obj_offset to a scalar.
obj_offset = self._CVXOPT_DENSE_INTF.scalar_value(obj_offset)
A, b = self._constr_matrix(constr_map[s.EQ], var_offsets, x_length,
self._CVXOPT_SPARSE_INTF,
self._CVXOPT_DENSE_INTF)
G, h = self._constr_matrix(constr_map[s.INEQ], var_offsets, x_length,
self._CVXOPT_SPARSE_INTF,
self._CVXOPT_DENSE_INTF)
# Save original cvxopt solver options.
old_options = cvxopt.solvers.options
# Silence cvxopt if verbose is False.
cvxopt.solvers.options['show_progress'] = verbose
# Always do one step of iterative refinement after solving KKT system.
cvxopt.solvers.options['refinement'] = 1
# Target cvxopt clp if nonlinear constraints exist
if constr_map[s.EXP]:
# Get the nonlinear constraints.
F = self._merge_nonlin(constr_map[s.EXP], var_offsets,
x_length)
# Get custom kktsolver.
kktsolver = get_kktsolver(G, dims, A, F)
results = cvxopt.solvers.cpl(c.T, F, G, h, A=A, b=b,
dims=dims, kktsolver=kktsolver)
else:
# Get custom kktsolver.
kktsolver = get_kktsolver(G, dims, A)
results = cvxopt.solvers.conelp(c.T, G, h, A=A, b=b,
dims=dims, kktsolver=kktsolver)
status = s.SOLVER_STATUS[s.CVXOPT][results['status']]
if status == s.OPTIMAL:
primal_val = results['primal objective']
value = self.objective._primal_to_result(
primal_val - obj_offset)
# Restore original cvxopt solver options.
cvxopt.solvers.options = old_options
if constr_map[s.EXP]:
ineq_dual = results['zl']
else:
ineq_dual = results['z']
return (status, value, results['x'], results['y'], ineq_dual)
else:
return (status, None, None, None, None)
def _solve(self, solver=s.ECOS, ignore_dcp=False, verbose=False):
"""Solves a DCP compliant optimization problem.
Saves the values of primal and dual variables in the variable
and constraint objects, respectively.
Args:
solver: The solver to use. Defaults to ECOS.
ignore_dcp: Overrides the default of raising an exception if
the problem is not DCP.
verbose: Overrides the default of hiding solver output.
Returns:
The optimal value for the problem, or a string indicating
why the problem could not be solved.
"""
if not self.is_dcp():
if ignore_dcp:
print ("Problem does not follow DCP rules. "
"Solving a convex relaxation.")
else:
raise Exception("Problem does not follow DCP rules.")
objective, constr_map, dims = self.canonicalize()
all_ineq = itertools.chain(constr_map[s.EQ], constr_map[s.INEQ])
var_offsets, x_length = self._get_var_offsets(objective, all_ineq)
c, obj_offset = self._constr_matrix([objective], var_offsets, x_length,
self._DENSE_INTF,
self._DENSE_INTF)
A, b = self._constr_matrix(constr_map[s.EQ], var_offsets, x_length,
self._SPARSE_INTF, self._DENSE_INTF)
G, h = self._constr_matrix(constr_map[s.INEQ], var_offsets, x_length,
self._SPARSE_INTF, self._DENSE_INTF)
# Save original cvxopt solver options.
old_options = cvxopt.solvers.options
# Silence cvxopt if verbose is False.
cvxopt.solvers.options['show_progress'] = verbose
# Always do one step of iterative refinement after solving KKT system.
cvxopt.solvers.options['refinement'] = 1
# Target cvxopt clp if nonlinear constraints exist
if constr_map[s.NONLIN]:
# Get the nonlinear constraints.
F = self._merge_nonlin(constr_map[s.NONLIN], var_offsets, x_length)
# Get custom kktsolver.
kktsolver = get_kktsolver(G, dims, A, F)
results = cvxopt.solvers.cpl(c.T, F, G, h, A=A, b=b,
dims=dims,kktsolver=kktsolver)
status = s.SOLVER_STATUS[s.CVXOPT][results['status']]
primal_val = results['primal objective']
# Target cvxopt solver if SDP or invalid for ECOS.
elif solver == s.CVXOPT or len(dims['s']) > 0 or min(G.size) == 0:
# Get custom kktsolver.
kktsolver = get_kktsolver(G, dims, A)
# Adjust tolerance to account for regularization.
cvxopt.solvers.options['feastol'] = 2*1e-6
results = cvxopt.solvers.conelp(c.T, G, h, A=A, b=b,
dims=dims, kktsolver=kktsolver)
status = s.SOLVER_STATUS[s.CVXOPT][results['status']]
primal_val = results['primal objective']
else: # If possible, target ECOS.
# ECHU: ecos interface has changed and no longer relies on CVXOPT
# as a result, we have to convert cvxopt data structures into
# numpy arrays
#
# ideally, CVXPY would no longer user CVXOPT, except when calling
# conelp
#
cnp, hnp, bnp = (np.fromiter(iter(x),
dtype=np.double,
count=len(x))
for x in (c, h, b))
Gp, Gi, Gx = G.CCS
m, n1 = G.size
Ap, Ai, Ax = A.CCS
p, n2 = A.size
Gp, Gi, Ap, Ai = (np.fromiter(iter(x),
dtype=np.int32,
count=len(x))
for x in (Gp, Gi, Ap, Ai))
Gx, Ax = (np.fromiter(iter(x),
dtype=np.double,
count=len(x))
for x in (Gx, Ax))
Gsp = sp.csc_matrix((Gx, Gi, Gp), shape=(m, n1))
if p == 0:
Asp = None
bnp = None
else:
Asp = sp.csc_matrix((Ax, Ai, Ap), shape=(p, n2))
# ECHU: end conversion
results = ecos.solve(cnp, Gsp, hnp, dims, Asp, bnp, verbose=verbose)
status = s.SOLVER_STATUS[s.ECOS][results['info']['exitFlag']]
primal_val = results['info']['pcost']
# Restore original cvxopt solver options.
cvxopt.solvers.options = old_options
if status == s.SOLVED:
self._save_values(results['x'], var_offsets.keys())
self._save_values(results['y'], constr_map[s.EQ])
if constr_map[s.NONLIN]:
self._save_values(results['zl'], constr_map[s.INEQ])
else:
self._save_values(results['z'], constr_map[s.INEQ])
return self.objective._primal_to_result(primal_val - obj_offset[0])
else:
return status
def _solve(self, solver=s.ECOS, ignore_dcp=False, verbose=False):
"""Solves a DCP compliant optimization problem.
Saves the values of primal and dual variables in the variable
and constraint objects, respectively.
Parameters
----------
solver : str, optional
The solver to use. Defaults to ECOS.
ignore_dcp : bool, optional
Overrides the default of raising an exception if the problem is not
DCP.
verbose : bool, optional
Overrides the default of hiding solver output.
Returns
-------
float
The optimal value for the problem, or a string indicating
why the problem could not be solved.
"""
if not self.is_dcp():
if ignore_dcp:
print ("Problem does not follow DCP rules. "
"Solving a convex relaxation.")
else:
raise Exception("Problem does not follow DCP rules.")
objective, constr_map, dims = self.canonicalize()
all_ineq = itertools.chain(constr_map[s.EQ], constr_map[s.INEQ])
var_offsets, x_length = self._get_var_offsets(objective, all_ineq)
c, obj_offset = self._constr_matrix([objective], var_offsets, x_length,
self._DENSE_INTF,
self._DENSE_INTF)
# Convert obj_offset to a scalar.
obj_offset = self._DENSE_INTF.scalar_value(obj_offset)
A, b = self._constr_matrix(constr_map[s.EQ], var_offsets, x_length,
self._SPARSE_INTF, self._DENSE_INTF)
G, h = self._constr_matrix(constr_map[s.INEQ], var_offsets, x_length,
self._SPARSE_INTF, self._DENSE_INTF)
# Save original cvxopt solver options.
old_options = cvxopt.solvers.options
# Silence cvxopt if verbose is False.
cvxopt.solvers.options['show_progress'] = verbose
# Always do one step of iterative refinement after solving KKT system.
cvxopt.solvers.options['refinement'] = 1
# Target cvxopt solver if SDP or invalid for ECOS.
if solver == s.CVXOPT or len(dims['s']) > 0 \
or min(G.shape) == 0 or constr_map[s.NONLIN]:
# Convert c,A,b,G,h to cvxopt matrices.
c, b, h = map(lambda vec:
self._CVXOPT_DENSE_INTF.const_to_matrix(vec,
convert_scalars=True),
[c, b, h])
A, G = map(lambda mat:
self._CVXOPT_SPARSE_INTF.const_to_matrix(mat,
convert_scalars=True),
[A, G])
# Target cvxopt clp if nonlinear constraints exist
if constr_map[s.NONLIN]:
# Get the nonlinear constraints.
F = self._merge_nonlin(constr_map[s.NONLIN], var_offsets,
x_length)
# Get custom kktsolver.
kktsolver = get_kktsolver(G, dims, A, F)
results = cvxopt.solvers.cpl(c.T, F, G, h, A=A, b=b,
dims=dims,kktsolver=kktsolver)
status = s.SOLVER_STATUS[s.CVXOPT][results['status']]
primal_val = results['primal objective']
else:
# Get custom kktsolver.
kktsolver = get_kktsolver(G, dims, A)
# Adjust tolerance to account for regularization.
cvxopt.solvers.options['feastol'] = 2*1e-6
results = cvxopt.solvers.conelp(c.T, G, h, A=A, b=b,
dims=dims, kktsolver=kktsolver)
status = s.SOLVER_STATUS[s.CVXOPT][results['status']]
primal_val = results['primal objective']
else: # If possible, target ECOS.
# Convert c,h,b to 1D arrays.
c, h, b = map(lambda mat: np.asarray(mat)[:, 0], [c.T, h, b])
results = ecos.solve(c, G, h, dims, A, b, verbose=verbose)
status = s.SOLVER_STATUS[s.ECOS][results['info']['exitFlag']]
primal_val = results['info']['pcost']
# Restore original cvxopt solver options.
cvxopt.solvers.options = old_options
if status == s.OPTIMAL:
self._save_values(results['x'], var_offsets.keys())
self._save_values(results['y'], constr_map[s.EQ])
if constr_map[s.NONLIN]:
self._save_values(results['zl'], constr_map[s.INEQ])
else:
self._save_values(results['z'], constr_map[s.INEQ])
self._value = self.objective._primal_to_result(
primal_val - obj_offset)
else:
self._handle_failure(status, var_offsets.keys(),
itertools.chain(constr_map[s.EQ], constr_map[s.INEQ]))
self._status = status
return self.value
def feasible_pathflows(graph,
l_obs,
obs=None,
update=False,
with_cell_paths=False,
with_ODs=False,
x_true=None,
wp_trajs=None):
"""Attempts to find feasible pathflows given partial of full linkflows
Parameters:
----------
graph: Graph object
l_obs: observations of link flows
obs: indices of the observed links
update: if True, update path flows in graph
with_cell_paths: if True, include cell paths as constraints
with_ODs: if True, include ODs in the constraints if no with_cell_paths or in the objective if with_cell_paths
"""
assert with_cell_paths or with_ODs # we must have some measurements!
n = graph.numpaths
# route to links flow constraints
A, b = linkpath_incidence(graph), l_obs
if obs: A = A[obs, :] # trim matrix if we have partial observations
Aineq, bineq = spmatrix(-1.0, range(n),
range(n)), matrix(0.0,
(n, 1)) # positive constraints
if not with_cell_paths: # if just with ODs flow measurements:
Aeq, beq = path_to_OD_simplex(graph) # route to OD flow constraints
else: # if we have cellpath flow measurements:
assert wp_trajs is not None
Aeq, beq = WP.simplex(graph,
wp_trajs) # route to cellpath flow constraints
if with_ODs: # if we have ODs + cellpaths measurements
T, d = path_to_OD_simplex(
graph) # route to OD flow constraints included in objective
A, b = matrix([A, T]), matrix(
[b, d]) # add the constraints to the objective
if x_true is not None:
err1 = np.linalg.norm(A * x_true - b, 1) / np.linalg.norm(b, 1)
err2 = np.linalg.norm(Aeq * x_true - beq) / np.linalg.norm(beq, 1)
assert err1 < TOL, 'Ax!=b'
assert err2 < TOL, 'Aeq x!=beq'
# construct objective for cvxopt.solvers.qp
Q, c = A.trans() * A, -A.trans() * b
#x = solvers.qp(Q + REG_EPS*spmatrix(1.0, range(n), range(n)), c, Aineq, bineq, Aeq, beq)['x']
# try with cvxopt.solvers.cp
def qp_objective(x=None, z=None):
if x is None: return 0, matrix(1.0, (n, 1))
f = 0.5 * x.trans() * Q * x + c.trans() * x
Df = (Q * x + c).trans()
if z is None: return f, Df
return f, Df, z[0] * Q
dims = {'l': n, 'q': [], 's': []}
x = solvers.cp(qp_objective,
G=Aineq,
h=bineq,
A=Aeq,
b=beq,
kktsolver=get_kktsolver(Aineq, dims, Aeq,
qp_objective))['x']
if update:
logging.info('Update link flows, delays in Graph.')
graph.update_linkflows_linkdelays(P * x)
logging.info('Update path delays in Graph.')
graph.update_pathdelays()
logging.info('Update path flows in Graph object.')
graph.update_pathflows(x)
#import ipdb
#rank = 5
#if with_ODs == False:
# ipdb.set_trace()
return x, rn.rank(matrix([A, Aeq])), n
def _solve(self, solver=s.ECOS, ignore_dcp=False, verbose=False):
"""Solves a DCP compliant optimization problem.
Saves the values of primal and dual variables in the variable
and constraint objects, respectively.
Parameters
----------
solver : str, optional
The solver to use. Defaults to ECOS.
ignore_dcp : bool, optional
Overrides the default of raising an exception if the problem is not
DCP.
verbose : bool, optional
Overrides the default of hiding solver output.
Returns
-------
float
The optimal value for the problem, or a string indicating
why the problem could not be solved.
"""
if not self.is_dcp():
if ignore_dcp:
print ("Problem does not follow DCP rules. "
"Solving a convex relaxation.")
else:
raise Exception("Problem does not follow DCP rules.")
objective, constr_map, dims = self.canonicalize()
all_ineq = itertools.chain(constr_map[s.EQ], constr_map[s.INEQ])
var_offsets, x_length = self._get_var_offsets(objective, all_ineq)
c, obj_offset = self._constr_matrix([objective], var_offsets, x_length,
self._DENSE_INTF,
self._DENSE_INTF)
# Convert obj_offset to a scalar.
obj_offset = self._DENSE_INTF.scalar_value(obj_offset)
A, b = self._constr_matrix(constr_map[s.EQ], var_offsets, x_length,
self._SPARSE_INTF, self._DENSE_INTF)
G, h = self._constr_matrix(constr_map[s.INEQ], var_offsets, x_length,
self._SPARSE_INTF, self._DENSE_INTF)
# Save original cvxopt solver options.
old_options = cvxopt.solvers.options
# Silence cvxopt if verbose is False.
cvxopt.solvers.options['show_progress'] = verbose
# Always do one step of iterative refinement after solving KKT system.
cvxopt.solvers.options['refinement'] = 1
# Target cvxopt solver if SDP or invalid for ECOS.
if solver == s.CVXOPT or len(dims['s']) > 0 \
or min(G.shape) == 0 or constr_map[s.NONLIN]:
# Convert c,A,b,G,h to cvxopt matrices.
c, b, h = map(lambda vec:
self._CVXOPT_DENSE_INTF.const_to_matrix(vec,
convert_scalars=True),
[c, b, h])
A, G = map(lambda mat:
self._CVXOPT_SPARSE_INTF.const_to_matrix(mat,
convert_scalars=True),
[A, G])
# Target cvxopt clp if nonlinear constraints exist
if constr_map[s.NONLIN]:
# Get the nonlinear constraints.
F = self._merge_nonlin(constr_map[s.NONLIN], var_offsets,
x_length)
# Get custom kktsolver.
kktsolver = get_kktsolver(G, dims, A, F)
results = cvxopt.solvers.cpl(c.T, F, G, h, A=A, b=b,
dims=dims,kktsolver=kktsolver)
status = s.SOLVER_STATUS[s.CVXOPT][results['status']]
primal_val = results['primal objective']
else:
# Get custom kktsolver.
kktsolver = get_kktsolver(G, dims, A)
# Adjust tolerance to account for regularization.
cvxopt.solvers.options['feastol'] = 2*1e-6
results = cvxopt.solvers.conelp(c.T, G, h, A=A, b=b,
dims=dims, kktsolver=kktsolver)
status = s.SOLVER_STATUS[s.CVXOPT][results['status']]
primal_val = results['primal objective']
else: # If possible, target ECOS.
# Convert c,h,b to 1D arrays.
c, h, b = map(lambda mat: np.asarray(mat)[:, 0], [c.T, h, b])
results = ecos.solve(c, G, h, dims, A, b, verbose=verbose)
status = s.SOLVER_STATUS[s.ECOS][results['info']['exitFlag']]
primal_val = results['info']['pcost']
# Restore original cvxopt solver options.
cvxopt.solvers.options = old_options
if status == s.OPTIMAL:
self._save_values(results['x'], var_offsets.keys())
self._save_values(results['y'], constr_map[s.EQ])
if constr_map[s.NONLIN]:
self._save_values(results['zl'], constr_map[s.INEQ])
else:
self._save_values(results['z'], constr_map[s.INEQ])
self._value = self.objective._primal_to_result(
primal_val - obj_offset)
else:
self._handle_failure(status, var_offsets.keys(),
itertools.chain(constr_map[s.EQ], constr_map[s.INEQ]))
self._status = status
return self.value