gm_hack.py

import cvxpy.utilities as u
import cvxpy.lin_ops.lin_utils as lu
from cvxpy.atoms.atom import Atom
from cvxpy.constraints import SOC
import math

class gm_constr(Atom):
    """ Geometric mean of two scalars; :math:`(x_1, \cdots, x_n)^{1/n}`. """
    def __init__(self, t, x, y):
        super(gm_constr, self).__init__(t, x, y)

    # Returns the geometric mean of x and y.
    def numeric(self, values):
        return 0

    # The shape is the common width and the sum of the heights.
    def shape_from_args(self):
        return u.Shape(1, 1)

    # Always unknown.
    def sign_from_args(self):
        return u.Sign.ZERO

    # Default curvature.
    def func_curvature(self):
        return u.Curvature.CONSTANT

    def monotonicity(self):
        return len(self.args)*[u.monotonicity.INCREASING]

    # Only scalar arguments are valid.
    def validate_arguments(self):
        if not self.args[0].is_scalar() or not self.args[1].is_scalar() or not self.args[2].is_scalar():
            raise TypeError("The arguments to gm_constr must resolve to scalars." )

    @staticmethod
    def graph_implementation(arg_objs, size, data):
        """Reduces the atom to an affine expression and list of constraints.
        Parameters
        ----------
        arg_objs : list
            LinExpr for each argument.
        size : tuple
            The size of the resulting expression.
        data :
            Additional data required by the atom.
        Returns
        -------
        tuple
            (LinOp for objective, list of constraints)
        """

        t = arg_objs[0]
        x = arg_objs[1]
        y = arg_objs[2]
        two = lu.create_const(2, (1, 1))
        
        # SOC(x + y, [y - x, 2*v])
        constraints = [
            SOC(lu.sum_expr([x, y]),
                [lu.sub_expr(y, x),
                 lu.mul_expr(two, t, (1, 1))])
        ]
        
        return (0, constraints)
        
        
x = cvx.Variable()
y = cvx.Variable()
t = cvx.Variable()

prob = cvx.Problem(cvx.Minimize(gm_constr(t,x,y)))
prob.get_problem_data('SCS')['dims']
# gives: SolverError: The solver SCS cannot solve the problem.

prob.get_problem_data('ECOS')['dims']
# gives: {'ep': 0, 'f': 0, 'l': 0, 'q': [], 's': []}
# so it looks like the constraints aren't registering