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A primal-dual interior-point method capable of rapidly detecting infeasibility for nonlinear programs. (arXiv:1807.02900v1 [math.OC])
来源于:arXiv
With the help of a logarithmic barrier augmented Lagrangian function, we can
obtain closed-form solutions of slack variables of logarithmic-barrier problems
of nonlinear programs. As a result, a two-parameter primal-dual nonlinear
system is proposed, which corresponds to the Karush-Kuhn-Tucker point and the
infeasible stationary point of nonlinear programs, respectively, as one of two
parameters vanishes. Based on this distinctive system, we present a primal-dual
interior-point method capable of rapidly detecting infeasibility of nonlinear
programs. The method generates interior-point iterates without truncation of
the step. It is proved that our method converges to a Karush-Kuhn-Tucker point
of the original problem as the barrier parameter tends to zero. Otherwise, the
scaling parameter tends to zero, and the method converges to either an
infeasible stationary point or a singular stationary point of the original
problem. Moreover, our method has the capability to rapidly detect the
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