Stochastic Zulfia Invexity in Mathematical Programming

In this paper Stochastic Zulfia Invexity is introduced for single objective stochastic pro-gramming. The stochastic kernel η(y, x∗, ω) is required to satisfy a stochastic Zulfia conditionof order two. It is shown that Karush-Kuhn-Tucker conditions are sufficient for global opti-mality without convexity assumptions. Deterministic Zulfia invexity is obtained for |Ω| = 1and Hanson invexity is obtained as limiting case κ → ∞. Fractional, Pareto and nonsmoothextensions are indicated as research directions.