New Methods for Large Scale Local and Global Optimization.

We have pursued all the topic areas described in the grant proposal during the period of this grant. These include global optimization methods for molecular cluster problems, global optimization methods for protein folding problems, smoothing methods for global optimization, other optimization topics from molecular chemistry, and related large-scale optimization topics. The largest amount of effort has gone into the construction of new global optimization methods for protein folding problems and the development of new smoothing approaches for global optimization. We have extended our stochasticperturbation approach to large-scale global optimization to deal with proteins, and have had very good success on initial test problems. We have also developed a new, analytic smoothing approach, investigated some fundamental properties of smoothing, and successfully incorporated our smoothing approach into our global optimization algorithm. The combination of smoothing and our stochasticperturbation approach is so far producing excellent results. A related accomplishment under this grant has been the successful application of our stochasticperturbation approach to distance geometry problems from molecular chemistry. Finally, we have developed unified limited memorytruncated Newton methods for large-scale unconstrained optimization that seem to combine many of the advantages of each approach.