Globally convergent modifications to the Method of Moving Asymptotes and the solution of the subproblems using trust regions: theoretical and numerical results

An alternative strategy to solve the subproblems of the Method of Moving Asymptotes (MMA) is presented, based on a trust-region scheme applied to the dual of the MMA subproblem. At each iteration, the objective function of the dual problem is approximated by a regularized spectral model. A globally convergent modification to the MMA is also suggested, in which the conservative condition is relaxed by means of a summable controlled forcing sequence. Another modification to the MMA previously proposed by the authors [\emph{Optim. Methods Softw.}, 25 (2010), pp. 883--893] is recalled to be used in the numerical tests. This modification is based on the spectral parameter for updating the MMA models, so as to improve their quality. The performed numerical experiments confirm the efficiency of the indicated modifications, especially when jointly combined. This report contains all the global convergence results and the complete set of numerical and graphical elements that sustain our performance analysis.