def _solve_isolating(self,*args):
"""
Description
-----------
Isolate parameters and then solve program.
Used by linearize method to obtain subgradient.
Arguments must be numbers. A very important
point is that solve_isolating introduces
equality constraints and places them at the
beginning of the constraint list. This is
later used to construct the subgradient.
"""
# Process input
if(len(args) != 0 and type(args[0]) is list):
args = args[0]
# Create argument list
arg_list = []
for arg in args:
if(np.isscalar(arg)):
arg_list += [arg]
elif(type(arg) is cvxpy_matrix):
(m,n) = arg.shape
for i in range(0,m,1):
for j in range(0,n,1):
arg_list += [arg[i,j]]
else:
raise ValueError('Arguments must be numeric')
# Check number of arguments
if(len(arg_list) != len(self.params)):
raise ValueError('Invalid number of arguments')
# Isolate parameters
p1_map = {}
new_constr = cvxpy_list([])
for p in self.params:
v = var('v_'+p.name)
p1_map[p] = v
new_constr += cvxpy_list([equal(v,p)])
new_p1 = prog((self.action,re_eval(self.obj,p1_map)),
new_constr+re_eval(self.constr,p1_map),
self.params, self.options,self.name)
# Substitute parameters with arguments
p2_map = {}
for k in range(0,len(arg_list),1):
p2_map[new_p1.params[k]] = arg_list[k]
new_p2 = prog((new_p1.action,re_eval(new_p1.obj,p2_map)),
re_eval(new_p1.constr,p2_map),
[],new_p1.options,new_p1.name)
# Solve program
obj,lagrange_mul_eq = solve_prog(new_p2)
self.lagrange_mul_eq = lagrange_mul_eq
return obj
def _solve_isolating(self, *args):
"""
Description
-----------
Isolate parameters and then solve program.
Used by linearize method to obtain subgradient.
Arguments must be numbers. A very important
point is that solve_isolating introduces
equality constraints and places them at the
beginning of the constraint list. This is
later used to construct the subgradient.
"""
# Process input
if (len(args) != 0 and type(args[0]) is list):
args = args[0]
# Create argument list
arg_list = []
for arg in args:
if (np.isscalar(arg)):
arg_list += [arg]
elif (type(arg) is cvxpy_matrix):
(m, n) = arg.shape
for i in range(0, m, 1):
for j in range(0, n, 1):
arg_list += [arg[i, j]]
else:
raise ValueError('Arguments must be numeric')
# Check number of arguments
if (len(arg_list) != len(self.params)):
raise ValueError('Invalid number of arguments')
# Isolate parameters
p1_map = {}
new_constr = cvxpy_list([])
for p in self.params:
v = var('v_' + p.name)
p1_map[p] = v
new_constr += cvxpy_list([equal(v, p)])
new_p1 = prog((self.action, re_eval(self.obj, p1_map)),
new_constr + re_eval(self.constr, p1_map), self.params,
self.options, self.name)
# Substitute parameters with arguments
p2_map = {}
for k in range(0, len(arg_list), 1):
p2_map[new_p1.params[k]] = arg_list[k]
new_p2 = prog((new_p1.action, re_eval(new_p1.obj, p2_map)),
re_eval(new_p1.constr, p2_map), [], new_p1.options,
new_p1.name)
# Solve program
obj, lagrange_mul_eq = solve_prog(new_p2)
self.lagrange_mul_eq = lagrange_mul_eq
return obj
def _get_equivalent(self):
"""
Description
-----------
Construct a new program by applying the
transform algorithm to the constraints.
None: It is assumed that the program
has been previously expanded.
"""
return prog((self.action, self.obj), transform(self.constr), [],
self.options)
def _get_equivalent(self):
"""
Description
-----------
Construct a new program by applying the
transform algorithm to the constraints.
None: It is assumed that the program
has been previously expanded.
"""
return prog((self.action,self.obj),
transform(self.constr),[],self.options)
def _get_expanded(self):
"""
Description
-----------
Construct a new program by applying the
expansion algorithm to the objective
and constraints.
"""
new_obj,new_eq = expand(self.obj)
more_constr = expand(self.constr)
return prog((self.action,new_obj),
more_constr+new_eq,[],self.options)
def _get_cvx_relaxation(self):
"""
Description
-----------
Construct a new program by choosing
the convex constraints and ignoring
the other ones.
Note: It is assumed that the program
has been expanded and transformed
previously.
"""
return prog((self.action, self.obj), self.constr._get_convex(), [],
self.options)
def _get_cvx_relaxation(self):
"""
Description
-----------
Construct a new program by choosing
the convex constraints and ignoring
the other ones.
Note: It is assumed that the program
has been expanded and transformed
previously.
"""
return prog((self.action,self.obj),
self.constr._get_convex(),[],self.options)
def is_dcp(self,args=None):
"""
Description
-----------
Checks if the program follows DCP rules.
If args is None, the check is done on the
body of the program. If args is a list of
arguments, the parameters are replaced
with the arguments and the check is done
on the resulting program. This function
is called with a list of arguments when
cvxpy_tree.is_dcp is executed.
Arguments
---------
args: List of arguments
"""
# No arguments: Check body of program
if(args == None):
if(self.action == MINIMIZE and
not self.obj.is_convex()):
return False
elif(self.action == MAXIMIZE and
not self.obj.is_concave()):
return False
else:
return self.constr.is_dcp()
# Arguments given: Replace parameters and then check
else:
# Check if some argument has parameters
if(len(cvxpy_list(args).get_params()) != 0):
return False
# Create a param-arg map
p_map = {}
for k in range(0,len(args),1):
p_map[self.params[k]] = args[k]
# Re-evaluate
new_p = prog((self.action,re_eval(self.obj,p_map)),
re_eval(self.constr,p_map))
# Check dcp on resulting program
return new_p.is_dcp()
def is_dcp(self, args=None):
"""
Description
-----------
Checks if the program follows DCP rules.
If args is None, the check is done on the
body of the program. If args is a list of
arguments, the parameters are replaced
with the arguments and the check is done
on the resulting program. This function
is called with a list of arguments when
cvxpy_tree.is_dcp is executed.
Arguments
---------
args: List of arguments
"""
# No arguments: Check body of program
if (args == None):
if (self.action == MINIMIZE and not self.obj.is_convex()):
return False
elif (self.action == MAXIMIZE and not self.obj.is_concave()):
return False
else:
return self.constr.is_dcp()
# Arguments given: Replace parameters and then check
else:
# Check if some argument has parameters
if (len(cvxpy_list(args).get_params()) != 0):
return False
# Create a param-arg map
p_map = {}
for k in range(0, len(args), 1):
p_map[self.params[k]] = args[k]
# Re-evaluate
new_p = prog((self.action, re_eval(self.obj, p_map)),
re_eval(self.constr, p_map))
# Check dcp on resulting program
return new_p.is_dcp()
def _pm_expand(self,constr):
"""
Description
-----------
Given the constraint, which must be in the form
self(args) operator variable, the parameters
are replaced with arguments and then the
partial minimization description of the program
is merged with the constraint.
Argument
--------
constr: cvxpy_constr of the form self(args)
operator variable.
"""
# Get arguments
args = constr.left.children
# Create arg-param map by position
p_map = {}
for k in range(0,len(args),1):
p_map[self.params[k]] = args[k]
# Create new program
new_p = prog((self.action,re_eval(self.obj,p_map)),
re_eval(self.constr,p_map),[],
self.options,self.name)
# Expand partial minimization
right = constr.right
new_constr = []
if(self.curvature == CONVEX):
new_constr += [less(new_p.obj,right)]
else:
new_constr += [greater(new_p.obj,right)]
new_constr += new_p.constr
# Return constraints
return cvxpy_list(new_constr)
def __call__(self, *args):
"""
Description
-----------
Call program with specified arguments.
Parameters are substituted with arguments.
If all arguments are numeric, the resulting
optimization program is solved. If some
arguments are object, a tree is returned.
Arguments
---------
args: List of arguments.
(Can be numbers or objects)
"""
# Process input
if (len(args) != 0 and type(args[0]) is list):
args = args[0]
# Create argument list
arg_list = []
for arg in args:
if (np.isscalar(arg) or type(arg).__name__ in SCALAR_OBJS):
arg_list += [arg]
elif (type(arg) is cvxpy_matrix
or type(arg).__name__ in ARRAY_OBJS):
(m, n) = arg.shape
for i in range(0, m, 1):
for j in range(0, n, 1):
arg_list += [arg[i, j]]
else:
raise ValueError('Invalid argument type')
# Check number of arguments
if (len(arg_list) != len(self.params)):
raise ValueError('Invalid argument syntax')
# Solve if numeric
if (len(arg_list) == 0
or reduce(lambda x, y: x and y,
map(lambda x: np.isscalar(x), arg_list))):
# Substitute parameters with arguments
p1_map = {}
for k in range(0, len(arg_list), 1):
p1_map[self.params[k]] = arg_list[k]
new_p = prog((self.action, re_eval(self.obj, p1_map)),
re_eval(self.constr, p1_map), [], self.options,
self.name)
# Solve program
obj, lagrange_mul_eq = solve_prog(new_p)
return obj
# Upgrade numbers to objects
for i in range(0, len(arg_list), 1):
if (np.isscalar(arg_list[i])):
arg_list[i] = cvxpy_obj(CONSTANT, arg_list[i],
str(arg_list[i]))
# Return tree
return cvxpy_tree(self, arg_list)
def scp(p,bad_constr,sol):
"""
Description: Sequential convex programming
algorithm. Solve program p and try to
enforce equality on the bad constraints.
Argument p: cvxpy_program is assumed to be in
expanded and equivalent format.
Argument bad_constr: List of nonconvex
constraints, also in expanded and equivalent
format.
Argument sol: Solution of relaxation.
"""
# Quit if program is linear
if(len(bad_constr) == 0):
if(not p.options['quiet']):
print 'Tightening not needed'
return True
# Get parameters
tight_tol = p.options['SCP_ALG']['tight tol']
starting_lambda = p.options['SCP_ALG']['starting lambda']
max_scp_iter = p.options['SCP_ALG']['max scp iter']
lambda_multiplier = p.options['SCP_ALG']['lambda multiplier']
max_lambda = p.options['SCP_ALG']['max lambda']
top_residual = p.options['SCP_ALG']['top residual']
# Construct slacks
slacks = [abs(c.left-c.right) for c in bad_constr]
# Print header
if(not p.options['quiet']):
print 'Iter\t:',
print 'Max Slack\t:',
print 'Objective\t:',
print 'Solver Status\t:',
print 'Pres\t\t:',
print 'Dres\t\t:',
print 'Lambda Max/Min'
# SCP Loop
lam = starting_lambda*np.ones(len(slacks))
for i in range(0,max_scp_iter,1):
# Calculate max slack
max_slack = max(map(lambda x:x.get_value(), slacks))
# Quit if status is primal infeasible
if(sol['status'] == 'primal infeasible'):
if(not p.options['quiet']):
print 'Unable to tighten: Problem became infeasible'
return False
# Check if dual infeasible
if(sol['status'] == 'dual infeasible'):
sol['status'] = 'dual inf'
sol['primal infeasibility'] = np.NaN
sol['dual infeasibility'] = np.NaN
# Print values
if(not p.options['quiet']):
print '%d\t:' %i,
print '%.3e\t:' %max_slack,
print '%.3e\t:' %p.obj.get_value(),
print ' '+sol['status']+'\t:',
if(sol['primal infeasibility'] is not np.NaN):
print '%.3e\t:' %sol['primal infeasibility'],
else:
print '%.3e\t\t:' %sol['primal infeasibility'],
if(sol['dual infeasibility'] is not np.NaN):
print '%.3e\t:' %sol['dual infeasibility'],
else:
print '%.3e\t\t:' %sol['dual infeasibility'],
print '(%.1e,%.1e)' %(np.max(lam),np.min(lam))
# Quit if max slack is small
if(max_slack < tight_tol and
sol['status'] == 'optimal'):
if(not p.options['quiet']):
print 'Tightening successful'
return True
# Quit if residual is too large
if(sol['primal infeasibility'] >= top_residual or
sol['dual infeasibility'] >= top_residual):
if(not p.options['quiet']):
print 'Unable to tighten: Residuals are too large'
return False
# Linearize slacks
linear_slacks = []
for c in bad_constr:
fn = c.left.item
args = c.left.children
right = c.right
line = fn._linearize(args,right)
linear_slacks += [line]
# Add linearized slacks to objective
sum_lin_slacks = 0.0
for j in range(0,len(slacks),1):
sum_lin_slacks += lam[j]*linear_slacks[j]
if(p.action == MINIMIZE):
new_obj = p.obj + sum_lin_slacks
else:
new_obj = p.obj - sum_lin_slacks
new_t0, obj_constr = expand(new_obj)
new_p = prog((p.action,new_t0), obj_constr+p.constr,[],p.options)
# Solve new problem
sol = solve_convex(new_p,'scp')
# Update lambdas
for j in range(0,len(slacks),1):
if(slacks[j].get_value() >= tight_tol):
if(lam[j] < max_lambda):
lam[j] = lam[j]*lambda_multiplier
# Maxiters reached
if(not p.options['quiet']):
print 'Unable to tighten: Maximum iterations reached'
if(sol['status'] == 'optimal'):
return True
else:
return False
def __call__(self,*args):
"""
Description
-----------
Call program with specified arguments.
Parameters are substituted with arguments.
If all arguments are numeric, the resulting
optimization program is solved. If some
arguments are object, a tree is returned.
Arguments
---------
args: List of arguments.
(Can be numbers or objects)
"""
# Process input
if(len(args) != 0 and type(args[0]) is list):
args = args[0]
# Create argument list
arg_list = []
for arg in args:
if(np.isscalar(arg) or
type(arg).__name__ in SCALAR_OBJS):
arg_list += [arg]
elif(type(arg) is cvxpy_matrix or
type(arg).__name__ in ARRAY_OBJS):
(m,n) = arg.shape
for i in range(0,m,1):
for j in range(0,n,1):
arg_list += [arg[i,j]]
else:
raise ValueError('Invalid argument type')
# Check number of arguments
if(len(arg_list) != len(self.params)):
raise ValueError('Invalid argument syntax')
# Solve if numeric
if(len(arg_list) == 0 or
reduce(lambda x,y: x and y,
map(lambda x: np.isscalar(x),arg_list))):
# Substitute parameters with arguments
p1_map = {}
for k in range(0,len(arg_list),1):
p1_map[self.params[k]] = arg_list[k]
new_p = prog((self.action,re_eval(self.obj,p1_map)),
re_eval(self.constr,p1_map),[],
self.options,self.name)
# Solve program
obj,lagrange_mul_eq = solve_prog(new_p)
return obj
# Upgrade numbers to objects
for i in range(0,len(arg_list),1):
if(np.isscalar(arg_list[i])):
arg_list[i] = cvxpy_obj(CONSTANT,
arg_list[i],
str(arg_list[i]))
# Return tree
return cvxpy_tree(self,arg_list)