Invex functions and constrained local minima

Invex functions and duality

“…Hanson [10] showed that a minimum was implied when convexity was replaced by a much weaker condition, called invex by Craven [4], [5]. For the problem, Minimize f o (x) subject to -g(x) e 5,…”

“…where S is a closed convex cone, the vector / = (/ 0 , g) is required to have a certain property, here called cone-invex, in relation to the cone R + X S. Some conditions necessary, or sufficient, for cone-invex were given in Craven [5]; see also Hanson and Mond [12]. However, it would be useful to characterize some recognizable classes of cone-invex functions.…”

Modi ed objective function approach for multitime variational problems

“…Among these generalizations, the notion of invexity was first introduced by Hanson [10]. The results developed by Hanson inspired a great deal of subsequent works, which have greatly expanded the role of invexity in optimization (see, for example, [2,6,7,12]). …”

Funções Invexas Diferenciáveis e o Teorema de Karush-Kuhn-Tucker1

“…Das considerações anteriores podemos notar o que resta da convexidade de F após o seu domínio ter sido distorcido por φ. Essa propriedadeé justamente a propriedade (1.1). Baseado nestas observações, Craven [4] chamou tal propriedade de invexity e denominou estas funções de invex functions (uma alusãoà invariante convexo). Em português, denominamos invexidade e funções invexas, respectivamente.…”