A Modified Augmented Lagrangian Merit Function, and Q-Superlinear Characterization Results for Primal-Dual Quasi-Newton Interior-Point Method for Nonlinear Programming
Garcia, Zeferino Parada
This work was also published as a Rice University thesis/dissertation: http://hdl.handle.net/1911/19195
Two classes of primal-dual interior-point methods for nonlinear programming are studied. The first class corresponds to a path-following Newton method formulated in terms of the nonnegative variables rather than all primal and dual variables. The centrality condition is a relaxation of the perturbed Karush-Kuhn-Tucker condition and primarily forces feasibility in the constraints. In order to globalize the method using a linesearch strategy, a modified augmented Lagrangian merit function is defined in terms of the centrality condition. The second class is the Quasi-Newton interior-point methods. In this class the well-known Boggs-Tolle-Wang characterization of Q-Superlinear convergence for Quasi-Newton method for equality constrained optimization is extended. Critical issues in this extension are the choice of the centering parameter, the choice of the steplength parameter, and the choice of the primary variables.
Citable link to this pagehttps://hdl.handle.net/1911/101891
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