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.

• 저널Management Science · 12(3) · 241–252
• 토픽Optimization and Mathematical Programming · Control and Systems Engineering
• DOI10.1287/mnsc.12.3.241
• 저자Béla Martos