def convexify_para_constr(self):
"""
input:
self: a constraint of a problem
return:
if the constraint is dcp, return itself;
otherwise, return
a convexified constraint
para: [left side, right side]
if the left/right-hand side of the the constraint is linearized,
left/right side = [zero order parameter, {variable: [value parameter, [gradient parameter]]}]
else,
left/right side = []
dom: domain
"""
if not self.is_dcp():
dom = [] # domain
para = [] # a list for parameters
if self.expr.args[0].curvature == 'CONCAVE': # left-hand concave
lin = linearize_para(self.expr.args[0]) # linearize the expression
left = lin[0]
para.append(
[lin[1], lin[2]]
) # [zero order parameter, {variable: [value parameter, [gradient parameter]]}]
for con in lin[3]:
dom.append(con)
else:
left = self.expr.args[0]
para.append(
[]
) # appending an empty list indicates the expression has the right curvature
if self.expr.args[
1].curvature == 'CONCAVE': # negative right-hand must be concave (right-hand is convex)
lin = linearize_para(self.expr.args[1]) # linearize the expression
neg_right = lin[0]
para.append([lin[1], lin[2]])
for con in lin[3]:
dom.append(con)
else:
neg_right = self.expr.args[1]
para.append([])
return left + neg_right <= 0, para, dom
else:
return self
def convexify_para_constr(self):
"""
input:
self: a constraint of a problem
return:
if the constraint is dcp, return itself;
otherwise, return
a convexified constraint
para: [left side, right side]
if the left/right-hand side of the the constraint is linearized,
left/right side = [zero order parameter, {variable: [value parameter, [gradient parameter]]}]
else,
left/right side = []
dom: domain
"""
if not self.is_dcp():
dom = [] # domain
para = [] # a list for parameters
if self.expr.args[0].curvature == 'CONCAVE': # left-hand concave
lin = linearize_para(self.expr.args[0]) # linearize the expression
left = lin[0]
para.append([lin[1],lin[2]]) # [zero order parameter, {variable: [value parameter, [gradient parameter]]}]
for con in lin[3]:
dom.append(con)
else:
left = self.expr.args[0]
para.append([]) # appending an empty list indicates the expression has the right curvature
if self.expr.args[1].curvature == 'CONCAVE': # negative right-hand must be concave (right-hand is convex)
lin = linearize_para(self.expr.args[1]) # linearize the expression
neg_right = lin[0]
para.append([lin[1],lin[2]])
for con in lin[3]:
dom.append(con)
else:
neg_right = self.expr.args[1]
para.append([])
return left + neg_right <= 0, para, dom
else:
return self
def convexify_para_obj(obj):
"""
input:
obj: an objective of a problem
return:
if the objective is dcp,
return the cost function (an expression);
if the objective has a wrong curvature,
return the linearized expression of the cost function,
the zeros order parameter,
the dictionary of parameters indexed by variables,
the domain
"""
if obj.is_dcp() == False:
return linearize_para(obj.expr)
else:
return obj.expr
def convexify_para_obj(obj):
"""
input:
obj: an objective of a problem
return:
if the objective is dcp,
return the cost function (an expression);
if the objective has a wrong curvature,
return the linearized expression of the cost function,
the zeros order parameter,
the dictionary of parameters indexed by variables,
the domain
"""
if obj.is_dcp() == False:
return linearize_para(obj.expr)
else:
return obj.expr