A primal-dual symmetric relaxation for homogeneous conic systems
The authors consider the feasibility (existence of non-trivial solutions) of a pair of alternative conic systems of constraints . That pair of conic systems is reformulated as a primal-dual pair of conic programs. Each of the conic programs corresponds to a natural relaxation of each of the two conic systems. When the considered closed convex cone is a self-scaled cone with a known self-scaled barrier, the conic programming reformulation can be solved via an interior-point algorithm. A central feature of this approach is the conditioning of the system of equations that arise at each interior-point iteration. The condition number of such system of equations grows in a controlled manner and remains bounded by a constant factor of the square of Renegar's condition number of the matrix of the considered system of equations throughout the entire algorithm.
scientific article; zbMATH DE number 5161133