Effective Minimization of Nonsmooth Functions in the Limit Analysis Problem for Dielectrics in Powerful Electric Fields

The problem of minimization of ill-conditioned functions is considered. This problem arises as a result of finite-element approximation of the limit analysis problem for dielectrics in powerful electric fields. The objective function is nonsmooth therefore a smooth regularization of finite-dimensional problem is used. As a result distinct ravine of objective function is acquired. Convergence of the gradient and the heave-ball methods in relation to its internal and optimization parameters are studied inside the numerical computing environment and fourth-generation programming language Matlab.