Smoothing quadratic regularization method for hemivariational inequalities.

Hemivariational inequalities arise in nonsmooth mechanics of solid involving nonmonotone and multi-valued mechanical relations. Typically, after the finite-element discretization, they lead to constrained nonsmooth nonconvex optimization problems with objective functions being the sum of quadratic functions and nonsmooth terms. In this paper, smoothing approximations are employed to solve the constrained nonsmooth nonconvex optimization problems. After properties of the smoothing functions are analysed, a smoothing quadratic regularization algorithm is presented and studied. The proposed algorithm can be implemented efficiently since the closed form solution is available at each iteration. Convergence of the algorithm is shown, and the worst-case complexity is investigated for reaching an ε-Clarke stationary point. A numerical example is reported to show the performance of the proposed method. [ABSTRACT FROM AUTHOR]