Nonlinear renormalization group flow and approximate solutions

We propose a self-consistent renormalization group prescription for the scalar field theory. The formalism coincides with the local potential approximation in the sharp-cutoff limit but differs from the smooth cutoff. We explore the dependence of the critical exponent upsilon on the smoothness parameter and the field of expansion. We use an optimization scheme based on the minimum sensitivity principle to ensure the most rapid convergence of upsilon with the polynomial truncation level.