Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)We introduce a new flexible inexact-restoration algorithm for constrained optimization problems. In inexact-restoration methods, each iteration has two phases. The first phase aims at improving feasibility and the second phase aims to minimize a suitable objective function. In the second phase, we also impose bounded deterioration of the feasibility, obtained in the first phase. Here, we combine the basic ideas of the Fischer-Friedlander approach for inexact-restoration with the use of approximations of the Lagrange multipliers. We present a new option to obtain a range of search directions in the optimization phase, and we employ the sharp Lagrangian as merit function. Furthermore, we introduce a flexible way to handle sufficient decrease requirements and an efficient way to deal with the penalty parameter. Global convergence of the new inexact-restoration method to KKT points is proved under weak constraint qualifications.1651 188208Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)CNPq [E-26/171.164/2003 - APQ1]FAPESP [2010/19720-5, 2013/05475-7]FAPESP [201307375-0]