def linearize(expr):
"""Returns the tangent approximation to the expression.
Gives an elementwise lower (upper) bound for convex (concave)
expressions. No guarantees for non-DCP expressions.
Returns None if cannot be linearized.
Args:
expr: An expression.
Returns:
An affine expression or None.
"""
expr = Constant.cast_to_const(expr)
if expr.is_affine():
return expr
else:
tangent = expr.value
if tangent is None:
raise ValueError(
"Cannot linearize non-affine expression with missing variable values."
)
grad_map = expr.grad
for var in expr.variables():
if grad_map[var] is None:
return None
elif var.is_matrix():
flattened = Constant(grad_map[var]).T*vec(var - var.value)
tangent = tangent + reshape(flattened, *expr.size)
else:
tangent = tangent + Constant(grad_map[var]).T*(var - var.value)
return tangent
def linearize(expr):
"""Returns the tangent approximation to the expression.
Gives an elementwise lower (upper) bound for convex (concave)
expressions. No guarantees for non-DCP expressions.
Returns None if cannot be linearized.
Args:
expr: An expression.
Returns:
An affine expression or None.
"""
expr = Constant.cast_to_const(expr)
if expr.is_affine():
return expr
else:
tangent = expr.value
if tangent is None:
raise ValueError(
"Cannot linearize non-affine expression with missing variable values."
)
grad_map = expr.grad
for var in expr.variables():
if grad_map[var] is None:
return None
elif var.is_matrix():
flattened = Constant(grad_map[var]).T * vec(var - var.value)
tangent = tangent + reshape(flattened, *expr.size)
else:
tangent = tangent + Constant(
grad_map[var]).T * (var - var.value)
return tangent
def linearize(expr):
"""Returns an affine approximation to the expression computed at the variable/parameter values.
Gives an elementwise lower (upper) bound for convex (concave)
expressions that is tight at the current variable/parameter values.
No guarantees for non-DCP expressions.
If f and g are convex, the objective f - g can be (heuristically) minimized using
the implementation below of the convex-concave method:
.. code :: python
for iters in range(N):
Problem(Minimize(f - linearize(g))).solve()
Returns None if cannot be linearized.
Args:
expr: An expression.
Returns:
An affine expression or None.
"""
expr = Constant.cast_to_const(expr)
if expr.is_affine():
return expr
else:
tangent = expr.value
if tangent is None:
raise ValueError(
"Cannot linearize non-affine expression with missing variable values."
)
grad_map = expr.grad
for var in expr.variables():
if grad_map[var] is None:
return None
elif var.is_matrix():
flattened = Constant(grad_map[var]).T * vec(var - var.value)
tangent = tangent + reshape(flattened, expr.shape)
else:
tangent = tangent + Constant(
grad_map[var]).T * (var - var.value)
return tangent
