Often the solution to these problems can be equivalently (or approximately) expressed and solved by converting the formulation to the unconstrained problem formula_82 where the Lagrange multiplier formula_83 is a non-negative constant that establishes the appropriate balance between rate and distortion. Solving the unconstrained problem is equivalent to finding a point on the convex hull of the family of solutions to an equivalent constrained formulation of the problem. However, finding a solution – especially a closed-form solution – to any of these three problem formulations can be difficult. Solutions that do not require multi-dimensional iterative optimization techniques have been published for only three probability distribution functions: the uniform, exponential, and Laplacian distributions. Iterative optimization approaches can be used to find solutions in other cases.