def graph_implementation(arg_objs, shape, data=None):
"""Reduces the atom to an affine expression and list of constraints.
minimize n^2 + 2M|s|
subject to s + n = x
Parameters
----------
arg_objs : list
LinExpr for each argument.
shape : tuple
The shape of the resulting expression.
data :
Additional data required by the atom.
Returns
-------
tuple
(LinOp for objective, list of constraints)
"""
M = data[0]
x = arg_objs[0]
n = lu.create_var(shape)
s = lu.create_var(shape)
two = lu.create_const(2, (1, 1))
if isinstance(M, Parameter):
M = lu.create_param(M, (1, 1))
else: # M is constant.
M = lu.create_const(M.value, (1, 1))
# n**2 + 2*M*|s|
n2, constr_sq = power.graph_implementation(
[n],
shape, (2, (Fraction(1, 2), Fraction(1, 2)))
)
abs_s, constr_abs = abs.graph_implementation([s], shape)
M_abs_s = lu.mul_expr(M, abs_s)
obj = lu.sum_expr([n2, lu.mul_expr(two, M_abs_s)])
# x == s + n
constraints = constr_sq + constr_abs
constraints.append(lu.create_eq(x, lu.sum_expr([n, s])))
return (obj, constraints)
def graph_implementation(arg_objs, size, data=None):
"""Reduces the atom to an affine expression and list of constraints.
Parameters
----------
arg_objs : list
LinExpr for each argument.
size : tuple
The size of the resulting expression.
data :
Additional data required by the atom.
Returns
-------
tuple
(LinOp for objective, list of constraints)
"""
x = arg_objs[0]
obj, abs_constr = abs.graph_implementation([x], x.size)
obj, sum_constr = sum_entries.graph_implementation([obj], (1, 1))
return (obj, abs_constr + sum_constr)
def graph_implementation(arg_objs, size, data=None):
"""Reduces the atom to an affine expression and list of constraints.
minimize n^2 + 2M|s|
subject to s + n = x
Parameters
----------
arg_objs : list
LinExpr for each argument.
size : tuple
The size of the resulting expression.
data :
Additional data required by the atom.
Returns
-------
tuple
(LinOp for objective, list of constraints)
"""
M = data
x = arg_objs[0]
n = lu.create_var(size)
s = lu.create_var(size)
two = lu.create_const(2, (1, 1))
if isinstance(M, Parameter):
M = lu.create_param(M, (1, 1))
else: # M is constant.
M = lu.create_const(M.value, (1, 1))
# n**2 + 2*M*|s|
n2, constr_sq = square.graph_implementation([n], size)
abs_s, constr_abs = abs.graph_implementation([s], size)
M_abs_s = lu.mul_expr(M, abs_s, size)
obj = lu.sum_expr([n2, lu.mul_expr(two, M_abs_s, size)])
# x == s + n
constraints = constr_sq + constr_abs
constraints.append(lu.create_eq(x, lu.sum_expr([n, s])))
return (obj, constraints)