Abstract

In this paper, the filter technique of Fletcher and Leyffer (1997) is used to globalize the primal-dual interior-point algorithm for nonlinear programming, avoiding the use of merit functions and the updating of penalty parameters. The new algorithm decomposes the primal-dual step obtained from the perturbed first-order necessary conditions into a normal and a tangential step, whose sizes are controlled by a trust-region type parameter. Each entry in the filter is a pair of coordinates: one resulting from feasibility and centrality, and associated with the normal step; the other resulting from optimality (complementarity and duality), and related with the tangential step. Global convergence to first-order critical points is proved for the new primal-dual interior-point filter algorithm.

Keywords

Interior point methodMathematicsNonlinear programmingDual (grammatical number)Mathematical optimizationFilter (signal processing)Convergence (economics)Point (geometry)Nonlinear systemApplied mathematicsComputer scienceGeometryEconomicsPhysics

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Year
2000
Type
article
Citations
41
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Michael Ulbrich, Stefan Ulbrich, L. N. Vicente (2000). A Globally Convergent Primal-Dual Interior-Point Filter Method for Nonconvex Nonlinear Programming. Rice University's digital scholarship archive (Rice University) .