A class of multi-parametric quadratic program with an uncertain objective function - Wei, Wei; Wu, Danman; Wang, Zhaojian; Shafie-khah, Miadreza; Catalão, João P.S. (Elsevier, 2020)
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.
Keywords: multi-parametric quadratic program; critical regions; objective uncertainty; residential energy system; optimisation; parameters; programming; parallel publishing; mathematics; application frameworks; linear programming; innovations; functions (mathematical methods); information technology architecture; fi=Sähkötekniikka|en=Electrical Engineering|