On the minimizing trajectory of convex functions with unbounded level sets

We consider a convex function f(x) with unbounded level sets. Many algorithms, if applied to this class of functions, do not guarantee convergence to the global infimum. Our approach to this problem leads to a derivation of the equation of a parametrized curve x(t), such that an infimum of f(x) along this curve is equal to the global infimum of the function on Rn. We also investigate properties of the vectors of recession, showing in particular how to determine a cone of recession of the convex function. This allows us to determine a vector of recession required to construct the minimizing trajectory.