bounded below

Global convergence for the algorithm is established under the assumption that the objective function is bounded from below, The authors also generalize the algorithm to constrained convex optimization and obtain the convergence that is the same as unconstrained algorithm.

此外还把算法推广到约束凸规划问题，得到了与无约束问题同样的收敛结果，如果约束是线性的，则算法是数值可行的。

Most work in application often uses second order moment method and point estimation and bounded below method.

工程中常用的β分布近似方法有二阶矩法和点估计下限法。

Secondly, we prove the certain populations of the system are bounded below and get sufficient conditions of permanent living of populations by applying comparison theorem.

其次利用比较定理证明了该系统确定的种群是有下界的，得到了种群永久生存的充分条件。

Let J' be a bounded below complex.

设J~+是下有界复形。

The sequences generated by the new algorithm are proved to converge to a new solution if the three conditions that the peak selection p is continuous, the separable condition and the energy functional is bounded below are all satisfied.

证明了新算法产生的点列在满足峰选择p连续、可分离条件以及能量泛函下方有界三个条件之下一定能收敛到新解。

Here, the nonlinear term is bounded below and need not be nonnegative.

这里，非线性项是下有界的并且不需要是非负的。

Bounded below Property of Composition Operator on Bloch Space in Cn Unit Ball

单位C~n球上Bloch空间上复合算子的下有界性