Abstract
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 \(\bar{x}\) , we aim to characterize the set of parameter values for which there exists a point \(\bar{y}\) such that \((\bar{x},\bar{y})\) 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.
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The research of Jian-zhong Zhang is supported by University Grant Council of Hong Kong under the grant CERG CityU 9041091. The research of Jin-bao Jian and Chun-ming Tang is supported by the National Natural Science Foundation of China (No. 10771040) and Guangxi Province Science Foundation (No. 0832052, 0728006).
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Zhang, Jz., Jian, Jb. & Tang, Cm. Inverse problems and solution methods for a class of nonlinear complementarity problems. Comput Optim Appl 49, 271–297 (2011). https://doi.org/10.1007/s10589-009-9294-x
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DOI: https://doi.org/10.1007/s10589-009-9294-x