On the Validity of Nonlinear and Nonsmooth Inequalities

In this article, a new approach is presented to survey the validity of the nonlinear and nonsmooth inequalities on a compact domain using optimization. Here, an optimization problem corresponding with the considered inequality is proposed and by solving of which, the validity of the inequality will be determined. The optimization problem, in smooth and nonsmooth forms, is solved by a linearization approach. The efficiency of presented approach is illustrated in some examples.