A sufficient condition for invexity
The authors consider the problem \[ (1)\quad \min f(x);\quad g(x)\leq 0,\quad x\in X\subset {\mathbb{R}}^ n. \] Invexity at a point u is defined as the existence of a function \(\eta\) (.,.) such that for all x: \(f(x)- f(u)\geq \nabla f(u)^ t\eta (x,u)\). This is a generalization of convexity. Also if at a solution (u,\(\lambda)\) of the first order optimality system, the invexity relation holds for f and all components of g with the same \(\eta\), then u is a global solution of (1). In this paper the authors give sufficient conditions for invexity involving the gradients and lower bounds on the second order variation of the data. As no examples are given it is not easy to evaluate the effectiveness of their results.
scientific article; zbMATH DE number 4099053