This project will develop large-scale parallel optimization methods that can rigorously find globally optimal solutions to nonlinear problems. Rigorous global search methods recursively partition the search domain, using problem structure to eliminate subdomains from further consideration. We have developed an initial parallel optimization strategy for nonlinear problems using the PICO branch-and-bound framework, which has been used to rigorously quantify the worst-case probability of an accidental pre-arming in nuclear devices.
This project will extend this global optimization solver in several ways: (1) integrate our solver with a mathematical modeling language like AMPL, which can automatically generate the expression graphs that are needed for PICO, (2) extend the capabilities of PICO to ensure robust, efficient performance (e.g. incorporate additional nonlinear bounding techniques, such as interval methods). (3) adapt PICO's parallelization strategies for this class of branch-and-bound solvers (e.g. this solver has a high amount of granularity in its parallelization).
We plan to work with academic collaborators on this work who have their own funding (e.g., E. Gatzke, US Carolina). Some of this work will leverage the public-domain COCONUT project, but we expect that much of it will require novel research and algorithmic development.
Staff: Erik G. Boman, David M. Gay, William E. Hart.
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