In this paper, we present a strategy for the exact solution of multiparametric quadratically constrained quadratic programs (mpQCQPs). Specifically, we focus on multiparametric optimization problems with a convex quadratic objective function, quadratic inequality and linear equality constraints, described by constant matrices. The proposed approach is founded on the expansion of the Basic Sensitivity Theorem to a second-order Taylor approximation, which enables the derivation of the exact parametric solution of mpQCQPs. We utilize an active set strategy to implicitly explore the parameter space, based on which (i) the complete map of parametric solutions for convex mpQCQPs is constructed, and (ii) the determination of the optimal parametric solution for every feasible parameter realization reduces to a nonlinear function evaluation. Based on the presented results, we utilize the second-order approximation to the Basic Sensitivity Theorem to expand to the case of nonconvex quadratic constraints, by employing the Fritz John necessary conditions. Example problems are provided to illustrate the algorithmic steps of the proposed approach.

在本文中，我们提出了一种精确求解多参数二次约束二次程序（mpQCQP）的策略。具体来说，我们关注具有凸二次目标函数，二次不等式和线性等式约束（由常数矩阵描述）的多参数优化问题。所提出的方法是基于将基本灵敏度定理扩展为二阶泰勒近似，从而可以推导mpQCQP的精确参数解。我们利用主动集策略隐式地探索参数空间，在此基础上（i）构建凸mpQCQP的参数解的完整图，以及（ii）确定每个可行参数实现的最佳参数解都可简化为非线性函数评估。根据给出的结果，我们通过使用Fritz John必要条件，利用基本灵敏度定理的二阶逼近将其扩展到非凸二次约束的情况。提供示例问题来说明所提出方法的算法步骤。