Criteria for quasi-convexity and pseudo-convexity: Relationships and comparisons

A first order criterion for pseudo-convexity and second order criteria for quasi-convexity and pseudo-convexity are given for twice differentiable functions on open convex sets. The relationships between these second order criteria and other known criteria are also analysed. Finally, the numbers of operations required to verify these criteria are calculated and compared.This research was supported by the Natural Sciences and Engineering Research Council Canada, Grant no. A8312, and by NATO Research Grant no. 1934.