This study focuses on allocation problems that have some of their constraints defined in terms of Leontief input-output matrices, known as Z-matrices. A few properties of these matrices are discussed and then applied to achieve a possible reduction in the dimensionality of the resource...

In this study we derive the order of convergence of some line search techniques based on fitting polynomials; using function values only. It is shown that the order of convergence increases with the degree of the polynomial. If viewed as a sequence, the orders approach the Golden Section Ratio...

Many nonlinear programming algorithms utilize a one-dimensional search along directions generated by the algorithm. This paper describes a method for performing this search. The method finds 3 points which bracket the minimum, fits a quadratic through them to yield a fourth point, then fits...