The gradient of the Moreau-Yosida approximation to a piecewise C2 convex function is studied in this paper. The piecewise smoothness of the gradient function is obtained by introducing a constraint qualification of the sequential constant rank. 对分片C2凸函数的Moreau-Yosida逼近研究了它的梯度性质,引进了序列常秩约束条件,在此条件下证明了梯度函数具有分片光滑性质。
Especially, the global convergence is obtained under a weak Mangasarian-Promovitz constraint qualification ( MFCQ) instead of the linearly independent constraint qualification ( LICQ). 特别地,用一个弱MFCQ代替线性无关约束规格(LICQ)得到算法的全局收敛性。
From its model, similar to the linear programming, it is known that the constraint qualification is not only nonlinearly but also convex. 从它的模型可以看出,它的约束条件和线性规划相比,既是非线性的也是凸约束。
Kuhn-Tucker Constraint Qualification for Reversed Geometric Programming 反向几何规划的Kuhn-Tucker约束品性
On first order constraint qualification 关于一阶约束品性
Under generalized Slater constraint qualification, Kuhn-Tucker necessary conditions for the mathematical program are established while its objective function and constraints function are both differentiable functions-( h,(?)). 当目标函数和约束函数均为(h,(?))-可微函数时,在广义Slater约束规格下,得到了相应规划问题取得最优解的Kuhn-Tucker必要条件。
We will see first that the true problem is stable under the smoothing perturbation if a given regular condition, which can be seen as an extension of the well known Robinson constraint qualification, holds with respect to the constraint system. 我们首先证明了如果给定在约束系统上的正则性条件成立,原问题在光滑扰动下是稳定的。
We study the method of expressing separation of duty constraint 、 qualification constraint of users and enforcement risk constraint in Alloy, discuss the methods of verifying the satisfiability of these constraints and analyzing the degree at which security constraints match security requirement. 研究了在Alloy中表达职责分离约束、用户资质约束和执行风险约束的方法,并讨论了验证这些约束的可满足性、分析与安全需求相匹配程度的方法。
And then, under the Slater type constraint qualification, the Kuhn-tucker type necessary conditions for set-valued optimization problem in the sense of Benson proper efficient elements is established; at the same time, we gain a sufficient conditions for Benson proper efficient elements. 然后,在Slater型约束规格下得到了集值优化问题Benson真有效元的Kuhn-Tucker型最优性必要条件;同时,我们给出了一个Benson真有效元的充分条件等。