广义互补问题一个新的等价转化及误差界估计

New Reformulation and Error Bound Estimation of the Generalized Nonlinear Complementarity Problem Over a Polyhedral Cone

将多面体锥上的广义互补问题等价地转化为一个混合互补形式的广义互补问题,然后利用混合互补问题的相关结论,给出了该转化形式下广义互补问题的误差界估计成立的两个充要条件:半稳定、2-正则。一般地,由半稳定可以得到2-正则,但反之不然。最后证明了在严格互补条件下二者等价。

The generalized nonlinear complementarity problem over a polyhedral cone （GNCP） is reformulated as a mixed complementarity problem（ MCP）, and then the error bound estimation of the GNCP based on the related results on the latter problem is estimated. To guarantee that the error bound estimation holds, the relations between the error bound, the semistability and 2-regularity of the solutions are discussed. In the end, the semistability,2- regularity and weak regularity are equivalent under the condition of strictcomplementarity.