Supplementary Materials of Distributed Very Large Scale Bundle Adjustment by Global Camera Consensus

We provide a proof for the following statement for nonconvex function in this section and the convergence statement of ADMM algorithm for the bundle adjustment objective function in section 3.1 of the paper body can be obtained by using the following statement. Theorem With the objective function in Eqn. 7 in the paper body in which the gradients of each function fi are local Lipschitz continuous with Lipschitz constant Li, let {xi} ⊂ R denote a sequence generated by the iterations in Eqn. 8, 9 and 10 in the paper body, where n is the dimension of variables and N is the number of split function. Then, there exists a ρ > max{Li, i = 1, ..., N}), such that the iterations in Eqn. 8, 9 and 10 in the paper body are guaranteed to converge to a local minimum of Eqn. 7 in the paper body. The convergence proof mainly refers to the convergence proof of ADMM on convex functions in the appendix of [2]. Note the right of Eqn. 8 in the paper body as Lρ (xi, z,yi), namely