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_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_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_power(expr):
p = expr.p
if p == 1:
return transform_expr(only_arg(expr))
if p == 0:
return expression.scalar_constant(1)
raise TransformError("Unexpected power exponent", expr)
def transform_power(expr):
p = expr.p
if p == 1:
return transform_expr(only_arg(expr))
if p == 0:
return expression.scalar_constant(1)
raise TransformError("Unexpected power exponent", expr)
def transform_norm_nuc(expr):
X = only_arg(expr)
m, n = dims(X)
T = epi_var(expr, "norm_nuc", size=(m+n, m+n))
obj = expression.multiply(
expression.scalar_constant(0.5),
expression.trace(T))
return obj, [
expression.semidefinite(T),
expression.eq_constraint(expression.index(T, 0, m, m, m+n), X)]
def transform_norm_nuc(expr):
X = only_arg(expr)
m, n = dims(X)
T = epi_var(expr, "norm_nuc", size=(m + n, m + n))
obj = expression.multiply(expression.scalar_constant(0.5),
expression.trace(T))
return obj, [
expression.semidefinite(T),
expression.eq_constraint(expression.index(T, 0, m, m, m + n), X)
]
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_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_power(expr):
p = expr.p
if p == 1:
return only_arg(expr)
one = expression.scalar_constant(1, size=dims(expr))
if p == 0:
return one, []
t = epi_var(expr, "power")
x = only_arg(expr)
if p < 0:
p, w = power_tools.pow_neg(p)
constrs = gm_constrs(one, [x, t], w)
if 0 < p < 1:
p, w = power_tools.pow_mid(p)
constrs = gm_constrs(t, [x, one], w)
if p > 1:
p, w = power_tools.pow_high(p)
constrs = gm_constrs(x, [t, one], w)
return t, constrs
def transform_power(expr):
p = expr.p
if p == 1:
return only_arg(expr)
one = expression.scalar_constant(1, size=dims(expr))
if p == 0:
return one, []
t = epi_var(expr, "power")
x = only_arg(expr)
if p < 0:
p, w = power_tools.pow_neg(p)
constrs = gm_constrs(one, [x, t], w)
if 0 < p < 1:
p, w = power_tools.pow_mid(p)
constrs = gm_constrs(t, [x, one], w)
if p > 1:
p, w = power_tools.pow_high(p)
constrs = gm_constrs(x, [t, one], w)
return t, constrs
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 transform_indicator(expr):
return expression.scalar_constant(0, size=dims(expr)), [expr]
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 transform_indicator(expr):
return expression.scalar_constant(0, size=dims(expr)), [expr]
