Parallel Numerical Optimization: Current Status and an Annotated Bibliography

Parallel computing is becoming a basic tool for research in several areas of computational mathematical programming. Algorithms and models that were intractable by the performance standards of von Neumann computers are becoming increasingly attractive. New algorithms are designed specifically for parallel architectures; the insight obtained from the design and implementation of such algorithms leads occasionally to improved sequential algorithms. Researchers report computational experiments with linear programming problems approaching a million variables and nonlinear problems with thousands of variables are solved routinely on state-of-the-art supercomputers. We classify and comment on the literature in parallel optimization with particular emphasis on the numerical and computational aspects of the field. Discussion of the parallel optimization literature is preceded by a tutorial on parallel computing in general. Work on the related areas of performance evaluation models, parallel linear algebra and ben...