A Globally Convergent Version of REQP for Constrained Minimization

This paper seeks to improve the theoretical basis for the nonlinearprogramming algorithm REQP. A modification to the standard formof the method is presented which allows global convergence tobe proved under assumptions that are more realistic than thosepreviously required. Essentially, the modification involvesan additional test after each step to determine whether satisfactoryprogress is being made. Reduction in the penalty parameter canonly take place after a step that is judged to be ‘successful’.Numerical examples are included which show how this modificationcan help to protect the method from being ‘trapped’close to a constraint at a nonoptimal point.