Decomposability in fixed point computation with applications and acceleration techniques

In the past decade, several complementary pivot algorithms have been developed to search for fixed points of certain functions and point to set maps on unbounded regions. This paper develops a structure (called decomposability), which, when present, enables one to work in a lower dimensional space when solving these problems. Several examples of where this structure arises in applications are presented. It is shown that under suitable circumstances, the general constrained optimization problem (that of optimizing an objective function subject to both equality and inequality constraints) may be formulated as a decomposèble fixed point problem. At the same time, an approximation technique is developed to potentially improve the efficiency of the complementary pivot algorithms.