LINEAR-PROGRAMMING VIA A NON-DIFFERENTIABLE PENALTY FUNCTION

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 methods admits nonsimplex steps, and this feature enables it to be readily generalized to quadratic programming. The method is competitive with the standard simplex method. Moreover, the method is numerically stable. Also, because of the approach taken in this algorithm, i. e. , that of nonlinear programming, the methods used here should be able to be extended readily to quadratic programming and to the minimization of a nonlinear function with linear constraints.