Inverse problems and solution methods for a class of nonlinear complementarity problems

In this paper, motivated by the KKT optimality conditions for a sort of quadratic programs, we first introduce a class of nonlinear complementarity problems (NCPs). Then we present and discuss a kind of inverse problems of the NCPs, i.e., for a given feasible decision $\overline{x}$ , we aim to characterize the set of parameter values for which there exists a point $\overline{y}$ such that $(\overline{x},\overline{y})$ forms a solution of the NCP and require the parameter values to be adjusted as little as possible. This leads to an inverse optimization problem. In particular, under 𝓁 ∞, 𝓁 1 and Frobenius norms as well as affine maps, this paper presents three simple and efficient solution methods for the inverse NCPs. Finally, some preliminary numerical results show that the proposed methods are very promising.