An Automatic and Unified Treatment for the Degeneracy of Geometric Program and its Implementation(Theory)

Abstract

In geometrical program, degenerated input needs to be dealt with exceptionally. Since there are large variety of degeneracies, it is difficult to deal with all of those degeneracies individually. Conventional unified treatments for degeneracies require programmers to rewrite a quite amount in each program while what we propose in this paper deals with degeneracies almost automatically avoiding the rewrite of the program in C. For geometric programs in C, we introduce a new class in C++, replace the type of some variables with it and make the programs deal with degeneracies by symbolic perturbation with operator overloading in C++.