First- and Second-Order Optimality Conditions for Quadratically Constrained Quadratic Programming Problems
研究了带有二次锥约束和额外几何约束的二次规划问题，在适当假设下建立了KKT点最优性的充要条件，并详细分析了两个二次等式约束及可同时对角化的情况。
Abstract We consider a quadratic programming problem with quadratic cone constraints and an additional geometric constraint. Under suitable assumptions, we establish necessary and sufficient conditions for optimality of a KKT point and, in particular, we characterize optimality by using strong duality as a regularity condition. We consider in details the case where the feasible set is defined by two quadratic equality constraints and, finally, we analyse simultaneous diagonalizable quadratic problems, where the Hessian matrices of the involved quadratic functions are all diagonalizable by means of the same orthonormal matrix.