In this talk, we establish some new necessary and sufficient optimality conditions for global optimization problems. We first establish a necessary and sufficient optimality conditions for general global optimization problems with terms of (ε, L)-subdifferential and (ε, L)-normal set. We then establish tractable optimality conditions for the problems of minimizing a weakly convex or concave function subject to standard constraints, such as box constraints, binary constraints, and simplex constraints. We finally derive a global optimality condition for quadratic problems with arbitrary constraint set, which is necessary and sufficient. Our main theoretical tool  for establishing these optimality conditions is abstract convexity.