Vertex Programs Research Articles

Errata

Erratum to B. Martos, “The Direct Power of Adjacent Vertex Programming Methods,” Management Science, 12 3, pp. 241–252.

The Direct Power of Adjacent Vertex Programming Methods

How far does the power of the adjacent vertex methods extend in solving non-linear programming problems? This question here gets a partial answer, being restricted to variables and objective functions which are continuous and excluding any transformation or approximation of the original system. The underlying concepts are that of quasi-concavity and quasi-monotonicity. Necessary and sufficient characteristics of the family of objective functions are given in due generality although in some cases subject to several differentiability assumptions. For these latter cases a simple criterion of vector selection is presented. Finally the problem of linear fractional programming is briefly discussed as an example.