Fréchet Second-Order Subdifferentials of Lagrangian Functions and Optimality Conditions
研究了无限维空间中抽象约束最小化问题的二阶最优性条件，目标函数仅需C1光滑，通过变分分析中的弗雷歇二阶次微分应用于拉格朗日函数，推广并改进了现有结果。
.We establish some new results on second-order (necessary and sufficient) optimality conditions for minimization problems with abstract constraints in infinite-dimensional spaces, where the objective functions are only assumed to be \(C^1\) -smooth. For doing so, we apply the concept of Fréchet (regular) second-order subdifferential from variational analysis to the Lagrangian function of the problem under investigation. Our results extend and refine several existing ones.Keywordsminimization problem on Banach spacescone constrainttangent setLagrange multiplierFréchet second-order subdifferentialsecond-order necessary optimality conditionsecond-order sufficient optimality conditionMSC codes90C3049K2749J5390C5626A27