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We present a nonmonotone trust region algorithm for nonlinear equality constrained optimization problems. In our algorithm, we use the average of the successive penalty function values to rectify the ratio of predicted reduction and the actual reduction. Compared with the existing nonmonotone trust region methods, our method is independent of the nonmonotone parameter. We establish the global convergence of the proposed algorithm and give the numerical tests to show the efficiency of the algorithm.

A Nonmonotone Trust Region Algorithm Based on the Average of the Successive Penalty Function Values for Nonlinear Optimization