Duality and Optimality Conditions

Consider the optimization problem Min f(x) subject to G(x) ≺0, (4.1.1) x∈ C where C is a convex closed cone in the Euclidean space ℝ n , f : ℝ n → ℝ and G : ℝ n → Y is a mapping from ℝ n into the space Y := S m of m x m symmetric matrices.