Browsing by Author "Vicente, Luis N."

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    A Globally Convergent Primal-Dual Interior-Point Filter Method for Nonconvex Nonlinear Programming
    (2000-04) Ulbrich, Michael; Ulbrich, Stefan; Vicente, Luis N.
    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.
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    Analysis of Inexact Trust-Region SQP Algorithms
    (1999-09) Heinkenschloss, Matthias; Vicente, Luis N.
    In this paper we study the global convergence behavior of a class of composite-step trust-region SQP methods that allow inexact problem information. The inexact problem information can result from iterative linear systems solves within the trust-region SQP method or from approximations of first-order derivatives. Accuracy requirements in our trust-region SQP methods are adjusted based on feasibility and optimality of the iterates. In the absence of inexactness our global convergence theory is equal to that of Dennis, El-Alem, Maciel (SIAM J. Optim. 7 (1997), 177-207). If all iterates are feasible, i.e., if all iterates satisfy the equality constraints, then our results are related to the known convergence analyses for trust-region methods with inexact gradient information for unconstrained optimization.