We discuss recent developments in the solution of distance geometry problems that arise in the interpretation of NMR data and in the determination of protein structures. Distance geometry problems give rise to global optimization problems with simple structure, but a large number of local minimizers.
We present algorithms for determining solutions to distance geometry problems, where upper and lower bounds are provided on the distance data. Our approach is based on using the Gaussian transform to map the original objective function into a smoother function with fewer minimizers, and using an optimization algorithm on the transformed function to trace the minimizers back to the original function.
We use limited-memory variable-metric methods and sparse Newton methods to trace solution curves. We present results for distance data derived from DNA protein fragments with up to 2,000 atoms.
This work is joint with Zhijun Wu.
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