Condition number complexity of an elementary algorithm for computing a reliable solution of a conic linear system

We develop an algorithm for resolving a conic linear system (FPd), which is a system of the form (FPd): b- Ax Cy X Cx, where Cx and Cy are closed convex cones, and the data for the system is d = (A, b). The algorithm "resolves " the system in that it either finds an-solution of (FPd) for a pre-specified tolerance, or demonstrates that (FPd) has no solution by solving an alternative dual system. The algorithm is based on a generalization of von Neumann's algorithm for linear inequalities. The number of iterations of the algorithm is essentially bounded by 0 (C(d)2 ln(C(d)) n (libi)) when (FPd) has a solution, and is bounded by O (C(d)2) when (FPd) has no solution, and so depends only on two numbers, namely the feasibility tolerance and the condition number C(d) of the data d = (A, b) (in addition to the norm of the vector b), and is independent of the dimensions of the problem. The quantity C(d) is the condition number of (FPd), originally defined by Renegar a