Second-Order Optimality Conditions for Infinite-Dimensional Quadratic Programs - An, Duong Thi Viet (Journal of optimization theory and applications, 2022)
Second-order necessary and sufficient optimality conditions for local solutions and locally unique solutions of generalized quadratic programming problems in Banach spaces are established in this paper. Since the decomposition procedures using orthogonality relations in Euclidean spaces and the compactness of finite-dimensional unit spheres, which worked well for finite-dimensional quadratic programs, cannot be applied to the Banach space setting, a series of new constructions and arguments are proposed. These results give a comprehensive extension of the corresponding theorems on finite-dimensional quadratic programs.