A Symbolic Procedure for Computing Semidefinite Program Duals

This article describes computer algebra algorithms and methodology which allow the user to automatically compute symbolic formulas for duals of semidefinite programs. The distinctive feature of our algorithms and implementation is that each matrix is treated as a single symbol (just as a human would do it); traditional computer algebra programs require that one specify the dimension of each matrix and then assign a separate symbol to each entry. This paper is part of a broader campaign to develop computer algebra algorithms, methodology, and implementation which allows users to convert many systems problems to linear matrix inequalities LMIs and to manipulate them symbolically