Line Search Filter Methods for Nonlinear Programming: Motivation and Global Convergence

  • Wächter A
  • Biegler L
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Abstract

Line search methods are proposed for nonlinear programming using
Fletcher and Leyffer's filter method {[} Math. Program., 91 ( 2002), pp.
239 - 269], which replaces the traditional merit function. Their global
convergence properties are analyzed. The presented framework is applied
to active set sequential quadratic programming (SQP) and barrier
interior point algorithms. Under mild assumptions it is shown that every
limit point of the sequence of iterates generated by the algorithm is
feasible, and that there exists at least one limit point that is a
stationary point for the problem under consideration. A new alternative
filter approach employing the Lagrangian function instead of the
objective function with identical global convergence properties is
briefly discussed.

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Authors

  • Andreas Wächter

  • Lorenz T. Biegler

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