Analysis of Generalized Pattern Searches

Analysis of Generalized Pattern Searches

This paper contains a new convergence analysis for the Lewis and Torczon GPS class of pattern search methods for linearly constrained optimization. The analysis is motivated by the desire to understand the behavior of the algorithm under hypotheses more consistent with properties satisfied in practice for a class of problems, discussed at various points in the paper, for which these methods are...

Generalized pattern searches with derivative information

A common question asked by users of direct search algorithms is how to use derivative information at iterates where it is available. This paper addresses that question with respect to Generalized Pattern Search (GPS) methods for unconstrained and linearly constrained optimization. Specifically this paper concentrates on the GPS poll step. Polling is done to certify the need to refine the curren...

Analysis of Generalized Pattern

Analysis of Generalized Pattern SearchesCharles

This paper contains a new analysis for the Generalized Pattern Search (GPS) methods of Torczon and Lewis and Torczon. The two novel aspects are that the proofs are much shorter, and they use weaker continuity assumptions. Speciically, under very mild conditions, the method nds an interesting limit point even if the objective function is not continuous and is even extended valued. If the objecti...

Generalized analysis of the direct weakly interacting massive particle searches

We perform a generalized analysis of data from WIMP search experiments for pointlike WIMPs of arbitrary spin and general Lorenz-invariant WIMP-nucleus interaction. We explicitly show that in the nonrelativistic limit only spin-independent ~SI! and spin-dependent ~SD! WIMP-nucleon interactions survive, which can be parametrized by only five independent parameters. We explore this five-dimensiona...