A class of multi-parametric quadratic program with an uncertain objective function. (12th July 2020) - Wei, Wei; Wu, Danman; Wang, Zhaojian; Shafie-khah, Miadreza; Catalão, João P.S.
Highlights: The property of solutions of a class of multi-parametric quadratic program with objective uncertainty. Variable and parameter transformations that reformulate the problem as a traditional one. Application of the proposed model to the economic evaluation of a residential energy system. Abstract: 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.