def solve(self, objective, constraints, cached_data, warm_start, verbose,
solver_opts):
"""Returns the result of the call to the solver.
Parameters
----------
objective : CVXPY objective object
Raw objective passed by CVXPY. Can be convex/concave.
constraints : list
The list of raw constraints.
Returns
-------
tuple
(status, optimal value, primal, equality dual, inequality dual)
"""
sym_data = self.get_sym_data(objective, constraints)
id_map = sym_data.var_offsets
N = sym_data.x_length
extractor = CoeffExtractor(id_map, N)
# Extract the coefficients
(Ps, Q, R) = extractor.get_coeffs(objective.args[0])
P = Ps[0]
q = np.asarray(Q.todense()).flatten()
r = R[0]
# Forming the KKT system
if len(constraints) > 0:
Cs = [extractor.get_coeffs(c._expr)[1:] for c in constraints]
As = sp.vstack([C[0] for C in Cs])
bs = np.array([C[1] for C in Cs]).flatten()
lhs = sp.bmat([[2 * P, As.transpose()], [As, None]], format='csr')
rhs = np.concatenate([-q, -bs])
else: # avoiding calling vstack with empty list
lhs = 2 * P
rhs = -q
warnings.filterwarnings('error')
# Actually solving the KKT system
try:
sol = SLA.spsolve(lhs.tocsr(), rhs)
x = np.array(sol[:N])
nu = np.array(sol[N:])
p_star = np.dot(x.transpose(), P * x + q) + r
except SLA.MatrixRankWarning:
x = None
nu = None
p_star = None
warnings.resetwarnings()
result_dict = {s.PRIMAL: x, s.EQ_DUAL: nu, s.VALUE: p_star}
return self.format_results(result_dict, None, cached_data)
def stuffed_objective(self, problem, inverse_data):
extractor = CoeffExtractor(inverse_data)
# Extract to c.T * x, store r
C, R = extractor.get_coeffs(problem.objective.expr)
c = np.asarray(C.todense()).flatten()
boolean, integer = extract_mip_idx(problem.variables())
x = Variable(inverse_data.x_length, boolean=boolean, integer=integer)
new_obj = c.T * x + 0
inverse_data.r = R[0]
return new_obj, x
def apply(self, problem):
inverse_data = InverseData(problem)
new_obj, new_var = self.stuffed_objective(problem, inverse_data)
# Form the constraints
extractor = CoeffExtractor(inverse_data)
new_cons = []
for con in problem.constraints:
arg_list = []
for arg in con.args:
A, b = extractor.get_coeffs(arg)
arg_list.append(reshape(A * new_var + b, arg.shape))
new_cons.append(con.copy(arg_list))
inverse_data.cons_id_map[con.id] = new_cons[-1].id
# Map of old constraint id to new constraint id.
inverse_data.minimize = type(problem.objective) == Minimize
new_prob = problems.problem.Problem(Minimize(new_obj), new_cons)
return new_prob, inverse_data