In Inexact-Restoration (IR) methods each iteration is divided in two phases. In the first phase one aims to sufficiently improve the feasibility with a bounded deterioration of the optimality. In the second phase one minimizes a suitable objective function without loosing much of the improvement obtained in the previous phase. In this work we introduce an improved line search IR algorithm, combining the basic ideas of the Fischer-Friedlander method with the use of Lagrange multipliers. We present a new option to obtain a range of search directions in the optimization phase and we introduce the use of the sharp Lagrangian as merit function. Furthermore, we introduce a more flexible way to handle with the requirement of the sufficient feasibility improvement and a more efficient way to deal with the penalty parameter. These modifications increase the chances that more promising steps be acceptable by the algorithm. Examples of the numerical behavior of the algorithm in multi-objective problems are reported.