Inequality/equality constrained optimization: an analytical robustness comparison of a feasibility method versus L1 sequential quadratic programming

In this work we present an analytical robustness comparison of two methods for inequality/equality constrained optimization or nonlinear programming. The methods compared are (1) a feasibility method (FM), and (2) sequential quadratic programming with an L1 merit function (L1-SQP). The problem statement assumptions include nonstationarity of constraint error norms except at zero constraint error, without which we are not aware of any algorithm that is provably guaranteed to converge to a tolerance-feasible stationary point of a penalty function or a Kuhn-Tucker point. Global convergence of FM is proved analytically. L1-SQP is shown to exhibit potential failure even from a feasible starting point, due to an onset of infeasible sub problems. We are not aware of an implementable SQP algorithm that has this provable global convergence property of FM.