Browsing by Author "Paroda Garcia, Zeferino"

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    A modified augmented Lagrangian merit function, and Q-superlinear characterization results for primal-dual Quasi-Newton interior-point method for nonlinear programming
    (1997) Paroda Garcia, Zeferino; Tapia, Richard A.
    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.