Semidefinite relaxations for semi-infinite polynomial programming

This paper studies how to solve semi-infinite polynomial programming (SIPP) problems by semidefinite relaxation method. We first introduce two SDP relaxation methods for solving polynomial optimization problems with finitely many constraints. Then we propose an exchange algorithm with SDP relaxations to solve SIPP problems with compact index set. At last, we extend the proposed method to SIPP problems with noncompact index set via homogenization. Numerical results show that the algorithm is efficient in practice.Comment: 23 pages, 4 figure

Non-spectator Contributions To The Lifetime of Λb\Lambda_{b}

In this work, we evaluate the contributions of non-spectator effects to the lifetimes of $\Lambda_b$ and B-mesons. Based on the well-established models and within a reasonable range of the concerned parameters, the contributions can reduce the lifetime of $\Lambda_b$ by $7 \sim 8$ compared to that of B-mesons which are not significantly affected. This might partly explain the measured ratio $\tau(\Lambda_{b})/\tau(B^{0})=0.79$ \cite{Data}, which has been a long-standing discrepancy between theory and experimental data