SDP全局误差界及其SDP广义弱尖锐性的刻画

The Characterization of SDP Global Error Bound and SDP Generalized Weak Sharp Minima

针对SDP问题下非可行点求解算法的研究,提出了SDP的一种广义弱尖锐极小性,同时也刻画了SDP的全局误差界;利用SDP全局误差界的定义,建立了在满足度量正则的条件下SDP广义弱尖锐性与剩余残差的全局误差界之间的充分、必要条件;通过在Slater约束条件不满足的情况下,得到了用SDP的全局误差界来刻画SDP广义弱尖锐性的结论;在度量正则性和凸分析的性质下,最后证明了SDP的全局误差界和广义弱尖锐性是相互等价的。

To solve the infeasible points of SDP a generalized weak sharp minimization of SDP is proposed,and the SDP global error bound is also described.By using the definition of SDP global error bound,a sufficient and necessary condition between SDP generalized weak sharp minima and the global error bound of residual residue is established under the condition of satisfying metric regularity. When the Slater constraint condition is not satisfied,the SDP global error bound can characterize SDP generalized weak sharp minima. Under the properties of metric regularity and convex analysis,it is proved that SDP global error bound and SDP generalized weak sharp minima are equivalent to each other.