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1)  equaiity and inequality constraints
等式和不等式约束
2)  inequality and equality constraints
不等式和等式约束
3)  inequality constraints
不等式约束
1.
For the cases of process model uncertainties and equipment leakage,a data reconciliation method with inequality constraints and its application examples were presented.
针对化工过程模型不确定和设备存在泄漏等情况,采用不等式约束进行数据校正,并且与传统的等式约束方法进行了实例对此。
2.
Inequality constraints were handled with the similar method as their equality counterparts in Lagrange multiplier method,while the multipliers associated with inequality constraints were written as a positive definite function of the originally-defined multipliers.
基于Lagrange乘子法中将与不等式约束相关的乘子定义为原乘子的正定函数,用同样的方法处理不等式约束和等式约束的构想,构造了一种新的Lagrange乘子法。
3.
A method for incorporating linear state inequality constraints in a Kalman filter is proposed and applied to turbofan engine health estimation.
提出了一种加入线性不等式约束的卡尔曼滤波方法,并用于涡扇发动机的健康状况估计。
4)  inequality restriction
不等式约束
1.
Aiming at the nonlinear optimization problems with inequality restriction,we analyzed why the convergence speed of the traditional complex shape arithmetic was slow.
针对不等式约束非线性最优化问题,分析了传统复合形算法收敛速度慢的原因,提出了一种称为复合形旋转方向搜索的新算法,给出了算法的迭代计算流程和程序框图。
2.
For the growth curve model with respect to inequality restriction:Y=XBZ+ε,ε~→~(0,σ~2VI),tr(NB)≥0,this paper gives the definition of general admissibility of linear estimates under the matrix loss function(d(Y)-KBL)(d(Y)-KBL) .
对于带有不等式约束的生长曲线模型:Y=XBZ+ε,ε~→~(0,σ~2VI),tr(NB)≥0,本文在矩阵损失函数(d-KBL)(d-KBL)′下。
3.
In this thesis,the admissibility and general admissibility of linear estimators in growth curve model with respect to inequality restriction are considered.
本文研究了带有不等式约束的生长曲线模型中线性估计的容许性与泛容许性问题。
5)  inequality constraint
不等式约束
1.
A new algorithm for solving inequality constraint optimization problem;
一种求解不等式约束优化问题的新算法
2.
This paper presents some approximate algorithms for minimax nonlinear programs with inequality constraints by using maximum entropy method and algorithms relevant to nonlinear programming with inequality constraints,and convergence theorems concerning these algorithms are given.
结合极大熵方法与不等式约束非线性规划的有关算法,提出了求解不等式约束极小极大非线性规划的一种近似法,并讨论了算法的有关收敛
3.
To inequality constraints, a check procedure and a penalty function procedure are proposed, and equality constraints are dealt with by a procedure of solving equations in which tear equations may be converged by an iterating way or a penalty function way.
在无约束非线性规划问题全局优化的模拟退火算法基础上,进行有约束问题求解的进一步探讨,对不等式约束条件提出了检验法和罚函数法的处理方法,对等式约束条件开发了罚函数法和解方程法的求解步骤,并进行了分析比较,从而形成了完整的求取非线性规划问题全局优化的模拟退火算法。
6)  linear inequality constraint
不等式约束
1.
An interior affine scaling subspace trust region method for nonlinear optimizations subject to linear inequality constraints;
线性不等式约束优化问题的仿射内点信赖域子空间算法
2.
An interior affine scaling indefinite dogleg path algorithm for nonlinear optimizations subject to linear inequality constraints;
线性不等式约束优化问题的仿射内点不定dogleg算法
3.
Interior affine scaling curvilinear path algorithm for nonlinear optimizations subject to linear inequality constraints;
仿射内点最优路径法解线性不等式约束的优化问题
补充资料:Harnack不等式(对偶Harnack不等式)


Harnack不等式(对偶Harnack不等式)
quality (dual Hatnack inequality) Harnack in-

【补注】一直到G的边界的H助nack不等式,见【AZI.l翻..‘不等式(对停H山丸朗k不等不)[ Har.改沁-勺函勺(d切红Hat’I犯‘k如为uaJ卿);rap.姗二p魄HcT助(月加湘oe)] 给出正调和函数的两个值之比u(x)/“(y)的上界和下界估计的一个不等式,由A.Hai,剐火(汇IJ)得到.令u)0是n维E议当d空间的区域G中的一个调和函数;令E。(y)是中心在点y处半径为;的球{x:}x一y!<;}.若闭包万了刃.CG,则对于所有的、“凡(,),o0是常数,亡“(省:,…,氛)是任一。维实向量,叉‘G.不等式(2)中的常数M仅依赖于又,A,算子L的低阶项系数的某些范数以及G的边界与g的边界之间的距离. fy,1, …粤馨 对于形如u:+Lu“0的一致抛物型方程(算子L的系数可以依赖于t)的非负解:(x,t),类似于1压ar-恤比不等式的不等式也成立.在此情形下,对于顶点在点(y,动处开口向下的抛物面(图a) {(x,t川x一,I’<。,(T一t),:一v,簇t簇:}的内部的点(x,t),只能有单边的不等式(fs」): u(x,r)(M妇(y,T),这里,M依赖于y,T,又,A,料,,,算子L的低阶项系数的某些范数,以及抛物面的边界与在其中“(义,t))0的区域的边界之间的距离.例如,如果在柱形区域 Q二Gx(a,b],中“〕O,此外,歹CG,并且如果刁G与刁g之间的距离不小于d(>0),而d充分小,那么在gx(a一矛,bJ中不等式 。(、.t、___/,、一。1,.:一:.八 1。,二之二止,二止匕成几11止二一一丈‘.+一+11 u气y,T)\下一I“/成立(协J).特别地,如果在Q中u)0(图b),且如果对于位于Q中的紧集Q,和QZ有 占“们山n(t一:)>0, (义,t)‘Q- (y.下)〔QZ那么有 n知Lxu(x,t)簇M nunu(x,t), (x,‘)‘QZ(x,‘)‘Q-其中M“M(占,Q,QI,QZ,L).函数 ·、·,‘卜exn(‘睿,、‘一暮“:)—对于任意的k,,…,气,它是热方程u,一△拟“0的解—表明在抛物型情形下双边估计的不可能性,
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