  We introduce a new regularization technique, using what we refer to as the
Steklov regularization function, and apply this technique to devise an
algorithm that computes a global minimizer of univariate coercive functions.
First, we show that the Steklov regularization convexifies a given univariate
coercive function. Then, by using the regularization parameter as the
independent variable, a trajectory is constructed on the surface generated by
the Steklov function. For monic quartic polynomials, we prove that this
trajectory does generate a global minimizer. In the process, we derive some
properties of quartic polynomials. Comparisons are made with a previous
approach which uses a quadratic regularization function. We carry out numerical
experiments to illustrate the working of the new method on polynomials of
various degree as well as a non-polynomial function.

Optimization and Control