Comparison between two augmented Lagrangian algorithms for a optimization problem with equality constraints (Q2831733)

The following optimization problem is considered: NEWLINE\[NEWLINE f(x) ~\longrightarrow~ \min NEWLINE\]NEWLINE subject to NEWLINE\[NEWLINE c_j(x) = 0, ~1\leq j \leq p ,~~ l_i \leq x_i \leq u_i,~1 \leq i \leq n, NEWLINE\]NEWLINE where the functions \(f: \mathbb R^n \longrightarrow \mathbb R\), \(c_j: \mathbb R^n \longrightarrow \mathbb R\) are twice continuously differentiable and some of the variables may have no upper or lower bound. The methods used in the paper to solve the optimization problems are based on sequential minimization of the augmented Lagrangian. The first one uses the method of conjugate gradients with incorporated the trust region strategy, the second one is based on the method of projected gradient. The authors compare the efficiency of the two algorithms with each other and further each of them with the third algorithm by \textit{L. Niu} and \textit{Y. Yuan} [J. Comput. Math. 28, No. 1, 72--86 (2010; Zbl 1224.90170)]. Theoretical comparison of the methods is illustrated by numerical results presented in the concluding part of the paper.NEWLINENEWLINEFor the entire collection see [Zbl 1319.34006].