The SEISCOPE optimization toolbox is a set of FORTRAN 90 routines, which implement first-order methods (steepest-descent and nonlinear conjugate gradient) and second-order methods ([Formula: see text]-BFGS and truncated Newton), for the solution of large-scale nonlinear optimization problems. An efficient line-search strategy ensures the robustness of these implementations. The routines are proposed as black boxes easy to interface with any computational code, where such large-scale minimization problems have to be solved. Traveltime tomography, least-squares migration, or full-waveform inversion are examples of such problems in the context of geophysics. Integrating the toolbox for solving this class of problems presents two advantages. First, it helps to separate the routines depending on the physics of the problem from the ones related to the minimization itself, thanks to the reverse communication protocol. This enhances flexibility in code development and maintenance. Second, it allows us to switch easily between different optimization algorithms. In particular, it reduces the complexity related to the implementation of second-order methods. Because the latter benefit from faster convergence rates compared to first-order methods, significant improvements in terms of computational efforts can be expected.
On the Evaluation Complexity of Constrained Nonlinear Least-Squares and General Constrained Nonlinear Optimization Using Second-Order Methods
