A Globally Convergent Version of REQP for Constrained Minimization

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Abstract
This paper seeks to improve the theoretical basis for the nonlinear programming algorithm REQP. A modification to the standard form of the method is presented which allows global convergence to be proved under assumptions that are more realistic than those previously required. Essentially, the modification involves an additional test after each step to determine whether satisfactory progress is being made. Reduction in the penalty parameter can only take place after a step that is judged to be ‘successful’. Numerical examples are included which show how this modification can help to protect the method from being ‘trapped’ close to a constraint at a nonoptimal point.

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