The nonlinear programming method of Wilson, Han, and Powell with an augmented Lagrangian type line search function. I. Convergence analysis (Q790580)

Comparative studies of codes for solving continuously differentiable nonlinear programs indicate that quadratic approximation methods are efficient and reliable. In this paper the author presents a convergence analysis of the method of \textit{R. B. Wilson, S.-P. Han} and \textit{M. J. D. Powell} [cf. the author's book: Nonlinear programming codes. Information, tests, performance (1980; Zbl 0435.90063)]. This analysis results in overcoming some of the theoretical disadvantages and in improvement of numerical performance of the method. This is achieved by replacing the exact \(L_ 1\)-penalty function by a differentiable augmented Lagrange function for the line search computation.