Effective Minimization of Ill-conditioned Functions

Abstract

The problem of minimization of ill-conditioned functions is considered. These functions are motivated by the limit analysis problem for dielectrics in powerful electric fields. From computing point of view a minimization of these functions is not following by standard methods because they are nonsmooth. Distinct ravine of objective function in combination with a high dimension variables requires a smooth regularisation of finite-dimensional problem. Convergence of heave-ball method in relation to it's internal parameters and optimization parameters are studied in numerical computing environment and fourth-generation programming language Matlab.