Convergence depth control for interior point methods

For practical applications, optimization algorithms may converge to the optimal solution unreasonably slowly because of factors such as the poor scaling, ill‐conditioning, errors in calculation, and so on. Most improvements during the optimization procedure are made within a small part of the total computation time. To relieve the heavy computational burden, it is necessary to balance the calculation accuracy and computation cost. The traditional termination criteria based on the Karush‐Kuhn‐Tucker conditions cannot appropriately meet this requirement. Convergence depth control (CDC) strategy for Reduced Hessian Successive Quadratic Programming (RSQP) was presented as an alternative measure in a previous study. This work incorporates interior point methods with the modified CDC strategy, which was tested through AMPL interface and Aspen Open Solvers interface. Related properties are proved.