Optimality tests for partitioning and sectional search algorithms

摘要

This paper revives a familiar idea for use in solving optimization problems, particularly unstructured nonlinear programs with many variables. The idea involves partitioning variables into groups and successively performing a sectional search with respect to one group at a time. The paper addresses various difficulties normally associated with this type of procedure, and proposes ways to solve them. These include testing optimality of the point at termination, and developing ways to restart the process upon finding that the terminating point is not optimal. The paper also briefly discusses some useful implications of the results on how to group variables in unstructured nonlinear programs so as to improve convergence.