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A brief history of integer and continuous nonlinear programming is presented as well as the current obstacles to practical use of these mathematical programming techniques It is forecast that the useful contributions to nonlinear programming actualls made in the next few years are more likely to he consolidations than theoretical breakthroughs These contributions are likely to be the documentation of standard test problems, construction of user oriented software, and comparisons of currently known algorithms to demonstrate which techniques are best for specific problems. [ABSTRACT FROM AUTHOR]

The article presents several examples of the generalized eigenvalues problem and how the Pencil procedure processed these examples for input into user-supplied eigenvalue routine. It presents examples with matrix roots, pencil roots and computer algorithms.