A Primal-dual Interior Method for Nonconvex Nonlinear Programming

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Abstract

Primal-dual interior methods for nonconvex nonlinear programming have recently been the subject of significant attention from the optimization community. Several different primal-dual methods have been suggested, along with some theoretical and numerical results. Although the underlying motivation for all of these methods is relatively uniform, there axe nonetheless substantive variations in crucial details, including the formulation of the nonlinear equations, the form of the associated linear system, the choice of linear algebraic procedures for solving this system, strategies for adjusting the barrier parameter and the Lagrange multiplier estimates, the merit function, and the treatment of indefiniteness. Not surprisingly, each of these choices can affect the theoretical properties and practical performance of the method. This paper discusses the approaches to these issues that we took in implementing a specific primal-dual method.