New Second-Order Optimality Conditions for a Class of Differentiable Optimization Problems

In the present paper, we focus on the optimization problems, where objective functions are Fréchet differentiable, and whose gradient mapping is locally Lipschitz on an open set. We introduce the concept of second‐order symmetric subdifferential and its calculus rules. By using the second‐order symmetric subdifferential, the second‐order tangent set and the asymptotic second‐order tangent cone, we establish some second‐order necessary and sufficient optimality conditions for optimization problems with geometric constraints. Examples are given to illustrate the obtained results.