LAUSR

This paper is concerned with the rank-deficient problem of least squares adjustment models with inequality constraints. First, the problem under study is transformed into a linear complementarity problem (LCP) with a P0-matrix (P0-LCP), which is a non-symmetric matrix whose principal minors are all nonnegative. Second, both Mangasarian’s symmetric successive over relaxation and a perturbed LCP with arbitrarily small perturbation are employed to solve the P0-LCP. As a result, a new iterative algorithm for rank-deficient adjustment models with inequality constraints is presented, and its convergence is proven. Finally, examples are given to demonstrate the efficiency of the proposed algorithm. It is shown that the proposed algorithm can not only assess the stability of points but also provide additional adjustment criteria to guarantee the uniqueness of solutions to the problem of rank-deficient free-network adjustment.