Optimization codes and modeling environment

For the numerical solution of all problems considered in the following section a combination of the AMPL [18] algebraic modeling language and the interior point solver LOQO [35] proved to be both convenient and powerful. In order to make the formulation of mathematical optimization problems generic and independent of both the actual solver used and the programming language it is written in, modeling languages were developed. AMPL provides interfaces to a large number of solvers, both commercial and free-for-research codes. We used the following codes for our numerical study: LANCELOT [17], MINOS [32], SNOPT [19], the convex QP-solver BPMPD [30], and LOQO [35]. LOQO grew out of an interior point LP optimizer to a convex QP and very recently to a general NLP solver implementing an interior point approach. Although the code is currently still being perfected it proved to be very efficient for the solution of large-scale nonlinear problems in the benchmarks of [31]. It was thus chosen for the following computations. Another feature that makes AMPL attractive and that was exploited is its automatic differentiation capability. Only functions for objective and constraints need to be provided.