A new Inexact Restoration method for problems with inaccuracies

In a recent paper, an Inexact Restoration method was proposed to solve continuous optimization problems with constraints, where the objective function and constraints are inaccurately evaluated. Although this paper shows good properties of complexity and worst-case convergence, its theory relies on an overly strong assumption about how feasibility should be treated with respect to the accuracy of constraints. In the present work we propose an alternative algorithm where the theoretical results of such a paper are maintained even without the restrictive hypothesis. In addition, we advanced new concepts of  optimality conditions and qualification of constraints for the problem of interest and performed numerical tests that attest to the plausibility of the strategy.