In this paper, a modified nonmonotone QP-free method without penalty function or filter is proposed for inequality constrained optimization. There is only two or three systems of linear equations with the same coefficients are solved at each iteration. We obtain a fundamental direction and the corresponding multiplier by the first equation, and then make full use of Lagrangian function information and multiplier to bend the search direction appropriately and obtain the search direction by the second linear equation. Moreover, the acceptable criterion of trial points is relaxed by the modified nonmonotone linear search technique. Under mild conditions, the global convergence of the algorithm is proved. Numerical results are given at the end of the paper.
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