Numerical comparisons of smoothing functions for optimal correction of an infeasible system of absolute value equations

Optimal correction of an infeasible system of absolute value equations (AVEs), leads into a nonconvex and nonsmooth fractional problem. Using Dinkelbach's approach, this problem can be reformulated to form a single variable equation. In this paper, first, we have smoothed the equation by considering four important and famous smoothing functions (see[2,23]) and thus, to solve it, a smoothing-type algorithm based on the Difference of Convex (DC) algorithm-Newtown methods is proposed. Finally, the randomly generated AVEs were compared to find the best smoothing function.