def transform_sum_largest(expr):
x = only_arg(expr)
k = expr.k
q = epi_var(expr, "sum_largest")
t = epi_var(expr, "sum_largest_t", size=dims(x))
obj = expression.add(expression.sum_entries(t),
expression.multiply(expression.scalar_constant(k), q))
constr = [
expression.leq_constraint(x, expression.add(t, q)),
expression.leq_constraint(expression.scalar_constant(0), t)
]
return obj, constr
def transform_sum_largest(expr):
x = only_arg(expr)
k = expr.k
q = epi_var(expr, "sum_largest")
t = epi_var(expr, "sum_largest_t", size=dims(x))
obj = expression.add(
expression.sum_entries(t),
expression.multiply(expression.scalar_constant(k), q))
constr = [
expression.leq_constraint(x, expression.add(t, q)),
expression.leq_constraint(expression.scalar_constant(0), t)]
return obj, constr
def transform_huber(expr):
n = epi_var(expr, "huber_n")
s = epi_var(expr, "huber_s")
# n**2 + 2*M*|s|
t, constr = transform_expr(
expression.add(
expression.power(n, 2),
expression.multiply(expression.scalar_constant(2 * expr.M),
expression.abs_val(s))))
# x == s + n
x = only_arg(expr)
constr.append(expression.eq_constraint(x, expression.add(s, n)))
return t, constr
def transform_quad_over_lin(expr):
assert len(expr.arg) == 2
x, y = expr.arg
assert dim(y) == 1
t = epi_var(expr, "qol", size=(1,1))
return t, [
expression.soc_constraint(
expression.add(y, t),
expression.vstack(
expression.add(y, expression.negate(t)),
expression.reshape(
expression.multiply(expression.scalar_constant(2), x),
dim(x), 1))),
expression.leq_constraint(expression.scalar_constant(0), y)]
def transform_huber(expr):
n = epi_var(expr, "huber_n")
s = epi_var(expr, "huber_s")
# n**2 + 2*M*|s|
t, constr = transform_expr(
expression.add(
expression.power(n, 2),
expression.multiply(
expression.scalar_constant(2*expr.M),
expression.abs_val(s))))
# x == s + n
x = only_arg(expr)
constr.append(expression.eq_constraint(x, expression.add(s, n)))
return t, constr
def transform_quad_over_lin(expr):
assert len(expr.arg) == 2
x, y = expr.arg
assert dim(y) == 1
t = epi_var(expr, "qol", size=(1, 1))
return t, [
expression.soc_constraint(
expression.add(y, t),
expression.hstack(
expression.add(y, expression.negate(t)),
expression.reshape(
expression.multiply(expression.scalar_constant(2), x), 1,
dim(x)))),
expression.leq_constraint(expression.scalar_constant(0), y)
]
def transform_problem(problem, params):
prox_rules = PROX_RULES + BASE_RULES
# Epigraph/cone rules
if params.use_epigraph:
prox_rules.append(epigraph)
prox_rules.append(prox_non_negative)
prox_rules.append(transform_cone)
f_exprs = list(transform_expr(prox_rules, problem.objective))
for constr in problem.constraint:
f_exprs += list(transform_expr(prox_rules, constr))
return expression.Problem(objective=expression.add(*f_exprs))
def transform_problem(problem, params):
prox_rules = PROX_RULES + BASE_RULES
# Epigraph/cone rules
if params.use_epigraph:
prox_rules.append(epigraph)
prox_rules.append(prox_non_negative)
prox_rules.append(transform_cone)
f_exprs = list(transform_expr(prox_rules, problem.objective))
for constr in problem.constraint:
f_exprs += list(transform_expr(prox_rules, constr))
return expression.Problem(objective=expression.add(*f_exprs))
def transform_hstack(expr):
m = dim(expr, 0)
n = dim(expr, 1)
offset = 0
add_args = []
for arg in expr.arg:
ni = dim(arg, 1)
add_args.append(
expression.linear_map(
linear_map.right_matrix_product(linear_map.index(slice(offset, offset + ni), n), m), transform_expr(arg)
)
)
offset += ni
return expression.add(*add_args)
def transform_hstack(expr):
m = dim(expr, 0)
n = dim(expr, 1)
offset = 0
add_args = []
for arg in expr.arg:
ni = dim(arg, 1)
add_args.append(
expression.linear_map(
linear_map.right_matrix_product(
linear_map.index(slice(offset, offset + ni), n), m),
transform_expr(arg)))
offset += ni
return expression.add(*add_args)
def transform_vstack(expr):
m = dim(expr, 0)
n = dim(expr, 1)
offset = 0
add_args = []
for arg in expr.arg:
mi = dim(arg, 0)
add_args.append(
expression.linear_map(
linear_map.left_matrix_product(
linear_map.transpose(
linear_map.index(slice(offset, offset + mi), m)), n),
transform_expr(arg)))
offset += mi
return expression.add(*add_args)
def transform_vstack(expr):
m = dim(expr, 0)
n = dim(expr, 1)
offset = 0
add_args = []
for arg in expr.arg:
mi = dim(arg, 0)
add_args.append(
expression.linear_map(
linear_map.left_matrix_product(
linear_map.transpose(
linear_map.index(slice(offset, offset+mi), m)),
n),
transform_expr(arg)))
offset += mi
return expression.add(*add_args)
def transform_problem(problem):
f_exprs = list(transform_expr(problem.objective))
for constr in problem.constraint:
f_exprs += list(transform_expr(constr))
return expression.Problem(objective=expression.add(*f_exprs))
def transform_add(expr):
return expression.add(*[promote(transform_expr(e), dim(expr)) for e in expr.arg])
def gm(t, x, y):
return expression.soc_elemwise_constraint(
expression.add(x, y), expression.add(x, expression.negate(y)),
expression.multiply(expression.scalar_constant(2), t))
def problem(self):
return expression.Problem(
objective=expression.add(*(f.expr for f in self.nodes(FUNCTION))),
constraint=[f.expr for f in self.nodes(CONSTRAINT)])
def transform_add(expr):
return expression.add(
*[promote(transform_expr(e), dim(expr)) for e in expr.arg])
def gm(t, x, y):
return expression.soc_elemwise_constraint(
expression.add(x, y),
expression.add(x, expression.negate(y)),
expression.multiply(expression.scalar_constant(2), t))