On the Formulation of the Primal-Dual Newton Interior-Point Method for Nonlinear Programming
In this work we first study in detail the formulation of the primal-dual interior-point method for linear programming. We show that, contrary to popular belief, it cannot be viewed as the damped Newton's method applied to the Karush-Kuhn-Tucker conditioned for the logarithmic barrier function problem. Next we extend the formulation to general nonlinear programming, and then validate this extension by demonstrating that this algorithm can be implemented so that it is locally and Q-quadratically convergent under only the standard Newton's method assumptions. We discuss the globalization of the algorithm and include considerable numerical experimentation.
Citable link to this pagehttps://hdl.handle.net/1911/101780
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