A Primal-Dual Interior Method for Nonconvex Nonlinear Programming

David M. Gay, Michael L. Overton, Margaret H. Wright

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, accompanied by theoretical and numerical results. Although the underlying motivation for these methods is relatively uniform, there are substantive variations, including formulation of the nonlinear equations, the form of the associated linear system, the choice of linear algebraic procedures, strategies for adjusting the barrier parameter and 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 describes the approaches taken to these issues in a specific primal-dual method.

Technical report 97-4-08, Computing Sciences Research, Bell Labs, Murray Hill, NJ, July 29, 1997

Contact: mhw@research.bell-labs.com