CRPC-TR92206:  PDS:  Direct Search Methods for Unconstrained Optimization 
on Either Sequential or Parallel Machines

Virginia Torczon

March, 1992

PDS is a collection of Fortran subroutines for solving unconstrained 
nonlinear optimization problems using direct search methods. The software 
is written so that execution on sequential machines is straightforward 
while execution on Intel distributed memory machines, such as the iPSC/2, 
the iPSC/860 or the Touchstone Delta, can be accomplished simply by 
including a few well-defined routines containing calls to Intel-specific 
Fortran libraries. Those interested in using the methods on other 
distributed memory machines, even something as basic as a network of 
workstations or personal computers, need only modify these few 
subroutines to handle the global communication requirements. Furthermore, 
since the parallelism is clearly defined at the "do-loop" level, it is a 
simple matter to insert compiler directives that allow for execution on 
shared memory parallel machines. Included here is an example of such 
directives, contained in comment statements, for execution on a Sequent 
Symmetry S81. 

PDS encompasses an entire class of general-purpose optimization methods 
which require only that the user provide a subroutine to evaluate the 
function. These methods require even less of the problem to be solved 
since direct search methods presume only that the function is continuous. 
Thus, parallel direct search methods are particularly effective on 
parameter estimation problems involving a relatively small number of 
parameters. They are also very interesting as parallel algorithms because 
they are perfectly scalable: they can use any number of processors 
regardless of the dimension of the problem to be solved and, in fact, 
tend to perform better as more processors are added.