On adjusting parameters in homotopy methods for linear programming
Several algorithms in optimization can be viewed as following a solution
as a parameter or set of parameters is adjusted to a desired value.
Examples include homotopy methods in complementarity problems and
path-following (infeasible-) interior-point methods. If we have a metric in
solution space that corresponds to the complexity of moving from one solution
point to another, there is an induced metric in parameter space,
which can be used to guide parameter-adjustment schemes. We investigate
this viewpoint for feasible- and infeasible- interior-point methods for
Technical Report 1170, School of Operations Research and Industrial
Engineering, Cornell University, Ithaca, NY 14853-3801.