The Direct Power of Adjacent Vertex Programming Methods

B. Martos
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B. Martos: Institute of Economics of the Hungarian Academy of Sciences, Budapest

Management Science, 1965, vol. 12, issue 3, 241-252

Abstract: 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.

Date: 1965
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