The convex case corresponds of course to η(x, u)≡x−u; but, as Hanson showed, invexity is sufficient to imply both weak duality and that the Kuhn-Tucker conditions are sufficient for global optimality.
It is shown here that elementary relaxations of the conditions defining invexity lead to modified invexity notions which are both necessary and sufficient for weak duality and Kuhn-Tucker sufficiency.
Key WordsInvexity convex mathematial programs Kuhn-Tucker conditions weak duality
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