Second‐Order Global Optimality Conditions for Optimization Problems

Second‐order optimality conditions are studied for the constrained optimization problem where the objective function and the constraints are compositions of convex functions and twice strictly differentiable functions. A second‐order sufficient condition of a global minimizer is obtained by introducing a generalized representation condition. Second‐order minimizer characterizations for a convex program and a linear fractional program are derived using the generalized representation condition