On a Lagrangian penalty function method for nonlinear programming problems (Q1186086)

\textit{Le D. Muu} and \textit{W. Oettli} [Numer. Funct. Anal. Optimization 10, No. 9/10, 1003-1017 (1989; Zbl 0703.49011)] have proposed a Lagrangian penalty function method for monotone variational inequalities in which for the convergence of the algorithm it is required that a penalized subproblem has a unique solution. The author first modifies the algorithm for convex programming to obtain a geometric rate of convergence. The author further shows that the special case of the algorithm proposed by Muu and Oettli as applied to nonconvex problems is still convergent without the coercivity and convexity assumptions.