arXiv subjects
Publications and source records attributed to Hehui Wang.
In this paper, we discuss the perturbation analysis of the extended vertical linear complementarity problem (EVLCP). Under the assumption of the row $\mathcal{W}$-property, several absolute and relative perturbation bounds of EVLCP are given, which can be reduced to some existing results. Some numerical examples are given to show the proposed bounds.
In this paper, by making use of this fact that for $a_{j}, b_{j}\in \mathbb{R}$, $j=1,2,\ldots,n$, there are $λ_{j}\in [0,1]$ with $\sum_{j=1}^{n}λ_{j}=1$ such that \[ \min_{1\leq j\leq n}\{a_{j}\}-\min_{1\leq j\leq n}\{b_{j}\}=\sum_{j=1}^{n}λ_{j}(a_{j}-b_{j}), \] some new error bounds of the extended vertical LCP under the row $\mathcal{W}$-property are obtained, which cover the error bounds in [Math. Program., 106 (2006) 513-525] and [Comput. Optim. Appl., 42 (2009) 335-352]. Not only that, these new error bounds skillfully avoid the inconvenience caused by the row rearrangement technique for error bounds to achieve the goal of reducing the computation workload, which was introduced in the latter paper mentioned above. Besides, with respect to the row $\mathcal{W}$-property, two new sufficient and necessary conditions are obtained.