from cvxpy.atoms import EXP_ATOMS, PSD_ATOMS, SOC_ATOMS
from cvxpy.constraints import ExpCone, PSD, SOC
from cvxpy.error import DCPError, DGPError, SolverError
from cvxpy.problems.objective import Maximize
from cvxpy.reductions import (Chain, Dcp2Cone,
FlipObjective, Dgp2Dcp, Qp2SymbolicQp,
CvxAttr2Constr, Complex2Real,
ConeMatrixStuffing, EvalParams,
QpMatrixStuffing)
from cvxpy.reductions.complex2real import complex2real
from cvxpy.reductions.qp2quad_form import qp2symbolic_qp
from cvxpy.reductions.solvers.constant_solver import ConstantSolver
from cvxpy.reductions.solvers.solver import Solver
from cvxpy.reductions.solvers import defines as slv_def
def construct_solving_chain(problem, candidates, gp=False):
"""Build a reduction chain from a problem to an installed solver.
Note that if the supplied problem has 0 variables, then the solver
parameter will be ignored.
Parameters
----------
problem : Problem
The problem for which to build a chain.
candidates : dict
Dictionary of candidate solvers divided in qp_solvers
and conic_solvers.
gp : bool
If True, the problem is parsed as a Disciplined Geometric Program
instead of as a Disciplined Convex Program.
Returns
-------
SolvingChain
A SolvingChain that can be used to solve the problem.
Raises
------
SolverError
Raised if no suitable solver exists among the installed solvers, or
if the target solver is not installed.
"""
reductions = []
if len(problem.variables()) == 0:
reductions += [ConstantSolver()]
return SolvingChain(reductions=reductions)
# TODO Handle boolean constraints.
if complex2real.accepts(problem):
reductions += [Complex2Real()]
if gp:
reductions += [Dgp2Dcp()]
if not gp and not problem.is_dcp():
append = ""
append = (" However, the problem does follow DGP rules. "
"Consider calling this function with `gp=True`.")
raise DCPError("Problem does not follow DCP rules." + append)
elif gp and not problem.is_dgp():
append = ""
if problem.is_dcp():
append = (" However, the problem does follow DCP rules. "
"Consider calling this function with `gp=False`.")
raise DGPError("Problem does not follow DGP rules." + append)
# Dcp2Cone and Qp2SymbolicQp require problems to minimize their objectives.
if type(problem.objective) == Maximize:
reductions += [FlipObjective()]
# First, attempt to canonicalize the problem to a linearly constrained QP.
solve_as_qp = candidates['qp_solvers'] and qp2symbolic_qp.accepts(problem)
if solve_as_qp:
reductions += [CvxAttr2Constr(),
Qp2SymbolicQp()]
else: # Canonicalize it to conic problem.
if not candidates['conic_solvers']:
raise SolverError("Problem could not be reduced to a QP, and no "
"conic solvers exist among candidate solvers "
"(%s)." % candidates)
else:
reductions += [Dcp2Cone(),
CvxAttr2Constr()]
# TODO remove this.
# Eliminate parameters.
if problem.parameters():
reductions += [EvalParams()]
# Conclude the chain with one of the following:
# (1) QpMatrixStuffing --> [a QpSolver],
# (2) ConeMatrixStuffing --> [a ConicSolver]
# First, attempt to canonicalize the problem to a linearly constrained QP.
if solve_as_qp:
solver = sorted(candidates['qp_solvers'],
key=lambda s: slv_def.QP_SOLVERS.index(s))[0]
solver_instance = slv_def.SOLVER_MAP_QP[solver]
reductions += [QpMatrixStuffing(),
solver_instance]
return SolvingChain(reductions=reductions)
if not candidates['conic_solvers']:
raise SolverError("Problem could not be reduced to a QP, and no "
"conic solvers exist among candidate solvers "
"(%s)." % candidates)
# Our choice of solver depends upon which atoms are present in the
# problem. The types of atoms to check for are SOC atoms, PSD atoms,
# and exponential atoms.
atoms = problem.atoms()
cones = []
if (any(atom in SOC_ATOMS for atom in atoms)
or any(type(c) == SOC for c in problem.constraints)):
cones.append(SOC)
if (any(atom in EXP_ATOMS for atom in atoms)
or any(type(c) == ExpCone for c in problem.constraints)):
cones.append(ExpCone)
if (any(atom in PSD_ATOMS for atom in atoms)
or any(type(c) == PSD for c in problem.constraints)
or any(v.is_psd() or v.is_nsd()
for v in problem.variables())):
cones.append(PSD)
# Here, we make use of the observation that canonicalization only
# increases the number of constraints in our problem.
has_constr = len(cones) > 0 or len(problem.constraints) > 0
for solver in sorted(candidates['conic_solvers'],
key=lambda s: slv_def.CONIC_SOLVERS.index(s)):
solver_instance = slv_def.SOLVER_MAP_CONIC[solver]
if (all(c in solver_instance.SUPPORTED_CONSTRAINTS for c in cones)
and (has_constr or not solver_instance.REQUIRES_CONSTR)):
reductions += [ConeMatrixStuffing(),
solver_instance]
return SolvingChain(reductions=reductions)
raise SolverError("Either candidate conic solvers (%s) do not support the "
"cones output by the problem (%s), or there are not "
"enough constraints in the problem." % (
candidates['conic_solvers'],
", ".join([cone.__name__ for cone in cones])))
[docs]class SolvingChain(Chain):
"""A reduction chain that ends with a solver.
Parameters
----------
reductions : list[Reduction]
A list of reductions. The last reduction in the list must be a solver
instance.
Attributes
----------
reductions : list[Reduction]
A list of reductions.
solver : Solver
The solver, i.e., reductions[-1].
"""
def __init__(self, problem=None, reductions=[]):
super(SolvingChain, self).__init__(problem=problem,
reductions=reductions)
if not isinstance(self.reductions[-1], Solver):
raise ValueError("Solving chains must terminate with a Solver.")
self.solver = self.reductions[-1]
[docs] def prepend(self, chain):
"""
Create and return a new SolvingChain by concatenating
chain with this instance.
"""
return SolvingChain(reductions=chain.reductions + self.reductions)
[docs] def solve(self, problem, warm_start, verbose, solver_opts):
"""Solves the problem by applying the chain.
Applies each reduction in the chain to the problem, solves it,
and then inverts the chain to return a solution of the supplied
problem.
Parameters
----------
problem : Problem
The problem to solve.
warm_start : bool
Whether to warm start the solver.
verbose : bool
Whether to enable solver verbosity.
solver_opts : dict
Solver specific options.
Returns
-------
solution : Solution
A solution to the problem.
"""
data, inverse_data = self.apply(problem)
solution = self.solver.solve_via_data(data, warm_start,
verbose, solver_opts)
return self.invert(solution, inverse_data)
[docs] def solve_via_data(self, problem, data, warm_start, verbose, solver_opts):
"""Solves the problem using the data output by the an apply invocation.
The semantics are:
.. code :: python
data, inverse_data = solving_chain.apply(problem)
solution = solving_chain.invert(solver_chain.solve_via_data(data, ...))
which is equivalent to writing
.. code :: python
solution = solving_chain.solve(problem, ...)
Parameters
----------
problem : Problem
The problem to solve.
data : map
Data for the solver.
warm_start : bool
Whether to warm start the solver.
verbose : bool
Whether to enable solver verbosity.
solver_opts : dict
Solver specific options.
Returns
-------
raw solver solution
The information returned by the solver; this is not necessarily
a Solution object.
"""
return self.solver.solve_via_data(data, warm_start, verbose,
solver_opts, problem._solver_cache)
