1) regularity condition
正则条件
1.
hrough determining the feasible descent direction and descent stepsize, thes paper proposes a mead of searching the satisfactory solutions of bilevel optimization problems directly under certain regularity conditions by virtue of the dirctional derivatives of the optimal solutions.
本文在一定的正则条件下，借助于最优解的方向导数，提出了通过确定可行下降方向和下降步长来直接搜索两层优化问题满意解的一种方法。
2.
The concept of regularity of feasible set is presented, under the regularity condition, the stability of more general probabilistic constrained programs problems is studied.
在原始规划可行集上引入了正则的概念,并在此正则条件下,研究了更一般的概率约束规划问题的稳定性。
2) regularity condition
正则性条件
1.
We also show that all quasi-ideal adequate transversals of an abundant semigroup which satisfies regularity condition are mutually isomorphic.
关于富足半群我们证明了:满足正则性条件的富足半群若含有拟理想恰当断面,则其所有拟理想恰当断面均同构。
3) Polya Conditon requla
Polya条件正则
4) left rgularity condition
左正则性条件
1.
A finite semigroup is an IC abundant semigroup satisfying the left rgularity condition if and only if it is an orthodox superabundant semigroup whose idempotents form a left regular band.
一个有限半群是满足左正则性条件的IC富足半群当且仅当它是一个幂等元形成左正则带的纯整超富足半群,但满足左正则性条件的无限IC富足半群不都是幂等元形成左正则带的纯整超富足半群。
5) weak regularity condition number
弱正则条件数
1.
The definitions of weakly regular SPN decomposition and weak regularity condition number are proposed.
给出一个解非光滑方程的信赖域算法，提出弱正则SPN分解和弱正则条件数的定义。
6) Sacks-Ylvisaker regularity conditions
Sacks-Ylvisaker正则条件
1.
It was studied the linear average n-widths in Lq-norm(1≤q≤+∞) of the space C~r([0,1]) equipped with the Gaussian measure which satisfied Sacks-Ylvisaker regularity conditions.
研究了Cr([0,1])空间赋以满足Sacks-Ylvisaker正则条件的Gauss测度在空间Lq([0,1])(1≤q≤+∞)中的平均线性n-宽度,通过利用再生核Hilbert空间的性质,以及Kolmogorovn-宽度和线性n-宽度之间的关系,得到了上述平均线性n-宽度的渐近阶。
2.
The average widths in Lq-norm(1Sacks-Ylvisaker regularity conditions,and get the asymptotic order are studied.
确定了赋以满足Sacks-Ylvisaker正则条件的Gauss测度的高维连续函数空间Cr([0,1]d)在Lebesgue可积空间Lq([0,1]d)(1
补充资料：凡事豫则立，不豫则废
1.谓做任何事情，事先谋虑准备就会成功，否则就要失败。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
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