Two-step algorithms for nonlinear optimization with structured applications

In this paper we propose extensions to trust-region algorithms in which the classical step is augmented with a second step that we insist yields a dec rease in the value of the objective function. The classical convergence the ory for trust-region algorithms is adapted to this class of two-step algori thms. The algorithms can be applied to any problem with variable(s) whose contrib ution to the objective function is a known functional form. In the nonlinea r programming package LANCELOT, they have been applied to update slack vari ables and variables introduced to solve minimax problems, leading to enhanc ed optimization efficiency. Extensive numerical results are presented to sh ow the effectiveness of these techniques.