Mathematical Sciences: Object Oriented Software Design for Optimization and Inverse Problems

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Symes 9627355 The investigator and his colleague aim to bridge the often large gap between ``off-the-shelf'' software packages for numerical optimization, on the one hand, and complex applications in science and engineering, on the other, through further development of the Hilbert Class Library, an object-oriented programming environment written in C++. This approach to programming expresses optimization algorithms in terms of their natural abstract components (vector addition, inner product, and so forth), without imposing unnecessary constraints on data structure and representation. Application software, on the other hand, can be written using the most suitable data structures, algorithms, and languages (various dialects of Fortran, for instance). The programming environment provides a flexible and largely automatic interface between the generic optimization code and the application-specific code. In addition to the elaboration of the basic class library, objectives of this proposal include the implementation of several modern algorithms for large-scale optimization, the design of a software toolkit that allows application programmers and numerical optimizers easy access to the HCL programming environment, and testing on a variety of realistic problems. For example, research in seismic data processing methods provided the original motivation for this project, and remains a principal target. Reuse of software is a long-standing goal of software engineering research, as software development and maintenance represents the bulk of the cost of computation. Object oriented programming designates an approach to software design that elevates reusability to the status of guiding principle. Traditional ("procedural") programming style embeds the internal details of data and algorithms in the interfaces between program parts. Object oriented programming hides or encapsulates these details, which permits program parts to be interchanged with considerably great er ease. For this and other reasons, object orientation has become the dominant methodology in commercial programming, especially for graphics applications. It has not up to now had much impact on scientific computation, which has an equally great need for reusable software. Many scientists do not use freely available high quality numerical programs, simply because the procedural style in which these programs are written makes them incompatible with natural data representations in such fields as computer aided design and manufacturing, materials science, and biotechnology. An object oriented framework for basic scientific computations, as proposed here, could lead to greatly enhanced interchange of software between numerical analysts and other scientists, and so improve the efficiency of computational research.