Abstract
A numerically stable form of an algorithm that is closely related to the work of Gill and Murray [5] and Conn [3] is presented. Among other reasons, the penalty function approach has never been available for linear programming in a viable sense because of the inherent nonlinearities introduced. The nondifferentiable penalty function is unique in that it is a piecewise linear function and hence maintains a computational efficiency comparable with, and in general, better than, the standard form. The method admits nonsimplex steps, and this feature enables it to be readily generalized to quadratic programming.
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