Hybrid subgradient and simulated annealing method for hemivariational inequalities

TL;DR

This paper introduces a hybrid global-local algorithm combining subgradient and simulated annealing techniques to efficiently solve hemivariational inequalities in contact mechanics, demonstrating improved performance over existing solvers.

Contribution

The paper presents a novel hybrid method integrating global search with local minimization for hemivariational inequalities, enhancing solution robustness and efficiency.

Findings

The proposed method outperforms selected solvers in contact mechanics problems.

The algorithm effectively balances global exploration and local refinement.

Numerical experiments validate the method's convergence and accuracy.

Abstract

In this paper, we employ a global aggregate subgradient method for the numerical solution of hemivariational inequality problems arising in contact mechanics. The method integrates a global search procedure to identify starting points for a local minimization algorithm. The algorithm consists of two types of steps: null steps and serious steps. In each null step, only two subgradients are utilized: the aggregate subgradient and the subgradient computed at the current iteration point, which together determine the search direction. Furthermore, we compare the performance of the proposed method with selected solvers using a representative contact mechanics problem as a case study.