Mesh-independence of Lagrange-SQP methods with Lipschitz-continuous Lagrange multiplier updates
An augmented Lagrange-SQP method with Lipschitz continuous Lagrange multiplier updates is analyzed. The approximation of this method is investigated, and convergence results are presented. A mesh-independence principle for the augmented Lagrange-SQP method is proved, which asserts that asymptotically the infinite-dimensional algorithm and finite-dimensional discretizations have the same convergence property. More precisely, for sufficiently small mesh-size there is at most a difference of one iteration step between the number of steps required by the infinite-dimensional method and its discretization to converge within a given tolerance epsilon > 0. The theoretical results are demonstrated numerically by a parameter identification problem.
mesh-independence parameter identification augmented lagrangian sqp methods