Argonne National Laboratory

Solving Derivative-Free Nonlinear Least Squares Problems with POUNDERS

TitleSolving Derivative-Free Nonlinear Least Squares Problems with POUNDERS
Publication TypeBook Chapter
Year of Publication2014
AuthorsWild, SM
Other NumbersANL/MCS-P5120-0414

Much of the research and software tools in derivative-free optimization focus on blackbox optimization problems. These are problems where the objective is effectively a blackbox function, such as the scalar-valued output of an executable-only code, of the inputs. In practice, however, one often has additional knowledge (e.g., sparsity structures, partial separability, nonlinearity, convexity, form of nonsmoothness) about the problem, while still not having access to complete derivative information. This knowledge, which we characterize as defining a greybox optimization problem, can be exploited to reduce the solve time and/or obtain more accurate solutions. On the other hand, when designing software for derivative-free optimization, one must balance the customization needed to exploit this type of information with the ease of use for a nonexpert user. Achieving this balance is especially challenging in derivative-free optimization because of the size and diversity of the user pool, which includes many application scientists and engineers. For these nonexperts, derivative-free optimization is often a gateway to algorithmic differentiation, nonlinear programming, and other areas of structure-exploiting optimization.