Method grad

cvxpy/transforms/partial_optimize.py:226–277

Gives the (sub/super)gradient of the expression w.r.t. each variable. Matrix expressions are vectorized, so the gradient is a matrix. None indicates variable values unknown or outside domain. Returns: A map of variable to SciPy CSC sparse matrix or None.

(self)

    @property
    def grad(self):
        """Gives the (sub/super)gradient of the expression w.r.t. each variable.

        Matrix expressions are vectorized, so the gradient is a matrix.
        None indicates variable values unknown or outside domain.

        Returns:
            A map of variable to SciPy CSC sparse matrix or None.
        """
        # Subgrad of g(y) = min f_0(x,y)
        #                   s.t. f_i(x,y) <= 0, i = 1,..,p
        #                        h_i(x,y) == 0, i = 1,...,q
        # Given by Df_0(x^*,y) + \sum_i Df_i(x^*,y) \lambda^*_i
        #          + \sum_i Dh_i(x^*,y) \nu^*_i
        # where x^*, \lambda^*_i, \nu^*_i are optimal primal/dual variables.
        # Add PSD constraints in same way.

        # Short circuit for constant.
        if self.is_constant():
            return u.grad.constant_grad(self)

        old_vals = {var.id: var.value for var in self.variables()}
        fix_vars = []
        for var in self.dont_opt_vars:
            if var.value is None:
                return u.grad.error_grad(self)
            else:
                fix_vars += [var == var.value]
        prob = Problem(self.args[0].objective,
                       fix_vars + self.args[0].constraints)
        prob.solve(solver=self.solver, **self._solve_kwargs)
        # Compute gradient.
        if prob.status in s.SOLUTION_PRESENT:
            sign = self.is_convex() - self.is_concave()
            # Form Lagrangian.
            lagr = self.args[0].objective.args[0]
            for constr in self.args[0].constraints:
                # TODO: better way to get constraint expressions.
                lagr_multiplier = self.cast_to_const(sign * constr.dual_value)
                prod = lagr_multiplier.T @ constr.expr
                if prod.is_scalar():
                    lagr += sum(prod)
                else:
                    lagr += trace(prod)
            grad_map = lagr.grad
            result = {var: grad_map[var] for var in self.dont_opt_vars}
        else:  # Unbounded, infeasible, or solver error.
            result = u.grad.error_grad(self)
        # Restore the original values to the variables.
        for var in self.variables():
            var.value = old_vals[var.id]
        return result

    @property
    def domain(self):