In this paper we analyze a class of multi-parametric quadratic program (mpQP) with parameters in the objective function. Except for parameters in coefficients associated with the linear term, the coefficient of the quadratic term, which is a positive definite matrix, is multiplied by a scalar parameter, while the quadratic coefficient of a standard mpQP is deterministic. We reveal the optimal solution is a linear fractional function in the parameters, and the critical regions remain polyhedral. The discussed mpQP can be reformulated as a standard mpQP via variable and parameter transformations. The proposed method is used to evaluate the economic operation of a residential energy system under time-and-level-of-use electricity pricing, highlighting the potential application in practical problems.

本文分析了目标函数中带有参数的一类多参数二次程序（mpQP）。除了与线性项相关的系数中的参数外，作为正定矩阵的二次项的系数乘以标量参数，而标准mpQP的二次项是确定性的。我们发现最优解是参数中的线性分数函数，并且关键区域保持多面体。可以通过变量和参数转换将讨论的mpQP重新构造为标准mpQP。所提出的方法用于评估按使用时间和等级使用电价的住宅能源系统的经济运行，突出了在实际问题中的潜在应用。