Relationships between pre-invex concepts Original Research Article

It is well known that some properties of convex optimization problems, especially sufficient conditions for optimality, and duality conditions, are preserved when convexity is weakened to pre-invexity. However, there are several distinct pre-invex concepts—B-vex, B-pre-invex, pre-univex, (p,r)(p,r)-pre-invex—and these are not equivalent. The pre-invexity concepts mentioned above have also some properties which are characteristic and invariant for functions belonging to these classes of functions.