A Primal-Dual Interior-Point Method for Nonconvex Optimization with Multiple Logarithmic Barrier Parameters and with Strong Convergence Properties

Thomas Urban, Andre Tits and Craigl Lawrence

It is observed that an algorithm proposed in the 1980s for the solution of nonconvex constrained optimization problems is in fact a primal-dual logarithmic barrier interior-point method closely related to methods under current investigation in the research community. Its main distinguishing features are judicious selection and update of the multiple barrier parameters (one per constraint), use of the objective function as merit function, and careful bending of the search direction. As a pay-off, global convergence and fast local convergence ensue. The purpose of this short note is to describe the algorithm in the interior-point framework and language and to provide a preliminary numerical evaluation. The latter shows that the method compares well with algorithms recently proposed by other research groups.

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