Simulation and optimization based on equation-oriented models benefit the most from advanced modeling and optimization methods.However

linearly dependent and inconsistent constraints that arise from poor models or nonlinear programming (NLP) algorithms result in failure in practice.A method to detect the inconsistent constraints in this case is proposed.The detection is based on the infeasible system identification of NLP solvers and takes advantage of the structure of linearly dependent systems.Efficiency of the detection process can be improved significantly through proper linear solver invocations.Numerical experiments on examples derived from CUTE and COPS test sets demonstrate the effectiveness of the proposed method.