Gradient+Based+Multi-Start+Optimization

Purpose
Gradient based algorithms, in general, tend to converge to local optima. However, the local optima found by these algorithms are not guaranteed to be the best solution (the global optima). There may be more local optima in the design space that are not found by a single run of the gradient based algorithm. Gradient Based Multi-Start is a method to address this problem of multiple local optima.

Description
GBMS runs a gradient based algorithm from multiple starting points to find out if multiple local optima exist.

The GBMS algorithm implemented with Optima2D and Jetstream uses the Sobol sequence to generate multiple starting points that span the design space. The gradient based optimization is run starting from each point to obtain information on: The Sobol sequence used allows the results from GBMS to be deterministic (so the results can be reproduced); and allows the method to be extended to a larger sample of starting points without needing to re-run the first few starting points.
 * the number of local optima
 * the relative success of each optima (value of objective function) and
 * how likely each local optima is found from a random starting point