A new finitely convergent algorithm for systems of nonlinear inequalities

In this work, combining the generalized projection techniques with the idea of a strongly sub-feasible direction method, a new algorithm for solving systems of nonlinear inequalities is presented. At each iteration of the proposed algorithm, the search direction is yielded by just one new explicit formula. The proposed algorithm is proved not only to possess global and strong convergence but also to be able to produce a solution in a finite number of iterations. Finally, some interesting numerical results are reported.