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sufficient optimality condition
相关语句
  最优性充分条件
     It is assumed that functions in mathematical programs arc continuously differentiable and have Lipschitzian continuous gradient functions . By use of Clarke's generalized Jacobian matrix, the second -order efficient optimality condition, second-order sufficient optimality condition of minimizing solution for nonlinear programs , and the Lipschitzian continuous property of local minimizing solution for nonlinear parametric programs are given . Then the chief results of Wang Jinde and Fiacco are extended .
     假定所讨论的数学规划问题其函数连续可微且有Lipschitz连续的梯度函数运用Clarke广义Jacobi矩阵,给出了非线性规划(NLP)问题解的二阶最优性必要条件二阶最优性充分条件及非线性参数规划问题解的Lipschitz连续性质,推广了王金德Fiacco的主要结果。
短句来源
     For set valued vector minimization problem with inequality constraint, a sufficient optimality condition theorem and a necessary Fritz John type optimality condition theorem is derived in terms of the generalized contingent epiderivative.
     用广义相依上导数 ,描述了含不等式约束的集值向量极小化问题的最优性充分条件与Fritz John型最优性必要条件。
短句来源
     Furthermore, under appropriate conditions, a necessary optimality condition of the Slater type and a sufficient optimality condition are obtained for a nonsmooth programming problem involving B_convex functions.
     并在适当条件下 ,给出了含有Lips chitzB_凸函数的非光滑规划问题的一个Slater型最优性必要条件和最优性充分条件
短句来源
  充分条件
     For a class of nondifferentiable and nonconvex multiobjective mathematical 0programming problem (VP), that is, the problem of minimizing a local Lipschitzian vector function subject to a set of differentiable nonlinear inequalities and equalities in a convex set, generalized Kuhn-Tucker type necessary and sufficient optimality condition, generalized saddle-point type necessary and sufficient optimality condition, generalized Lagrange duality and generalized Mond-Weir duality are concerned. The dissertation consists of four chapters.
     本论文讨论一类在凸集上目标函数为Lipschitz连续的向量函数的带有可微不等式约束及可微等式约束的非线性多目标规划问题(VP),这是一类非凸非可微多目标规划问题。 本论文讨论了广义Kuhn-Tucker型最优性必要条件及充分条件,广义鞍点型最优性条件,广义Lagrange型对偶理论以及广义Mond-Weir型对偶理论,共分四部分。
短句来源
     It is assumed that functions in mathematical programs arc continuously differentiable and have Lipschitzian continuous gradient functions . By use of Clarke's generalized Jacobian matrix, the second -order efficient optimality condition, second-order sufficient optimality condition of minimizing solution for nonlinear programs , and the Lipschitzian continuous property of local minimizing solution for nonlinear parametric programs are given . Then the chief results of Wang Jinde and Fiacco are extended .
     假定所讨论的数学规划问题其函数连续可微且有Lipschitz连续的梯度函数运用Clarke广义Jacobi矩阵,给出了非线性规划(NLP)问题解的二阶最优性必要条件二阶最优性充分条件及非线性参数规划问题解的Lipschitz连续性质,推广了王金德Fiacco的主要结果。
短句来源
     On the basis of its main vesult,the kuhn-Tuches second order sufficient optimality condition implies the existence of exact iceal penalty functions under convexity of the penalty term In this paper, we develop this theory constantly, increase a constrained condition x∈X and omit convexity of the penalty term Q,tinally,we obtain sesult ofsimilar the paper [1].
     根据其的主要结论所证明的若惩罚项Q是凸函数,则K-T二阶充分条件可以保证局部精确罚函数存在,对此继续作了进一步推广,增加了约束条件x∈X,并且去掉了Q的凸性假设,对于这种更一般的模型,同样证明了文献[1]中的相应结论。
短句来源
     For set valued vector minimization problem with inequality constraint, a sufficient optimality condition theorem and a necessary Fritz John type optimality condition theorem is derived in terms of the generalized contingent epiderivative.
     用广义相依上导数 ,描述了含不等式约束的集值向量极小化问题的最优性充分条件与Fritz John型最优性必要条件。
短句来源
     Furthermore, under appropriate conditions, a necessary optimality condition of the Slater type and a sufficient optimality condition are obtained for a nonsmooth programming problem involving B_convex functions.
     并在适当条件下 ,给出了含有Lips chitzB_凸函数的非光滑规划问题的一个Slater型最优性必要条件和最优性充分条件
短句来源
  “sufficient optimality condition”译为未确定词的双语例句
     Sufficient Optimality Condition of Nonsmooth V - ρ - in vex Multiobjective Programming
     复合V-ρ不变凸多目标规划最优充分性条件
短句来源
     2. Chapter3, being the main part of this dissertation, converts nonconvex semidefinite programming problem (SDP) to nonlinear programming problem (ESDP), and proves that under transversality condition, strict complementarity condition and the sufficient optimality condition of local solutions, (SDP) and (ESDP) are equivalent locally.
     2.第3章是本文的主要部分,将非凸半定规划问题(SDP)转化为等式约束的非线性规划问题(ESDP),并证明了在(SDP)局部解的充分性条件及严格互补松弛与非退化条件之下两问题的局部等价性。
短句来源
     THE SUFFICIENT OPTIMALITY CONDITION FOR A CLASS OF MATHEMATICAL PROGRAMS AND ITS APPLICATION TO STOCHASTIC PROGRAMMING
     一类数学规划问题的最优性充分条件及其在随机规划中的应用
短句来源
     On the basis of presented results ,the paper study some optimal control quantity about Burgers equation include giving the F-derivatives of J and e, proving the regular point condition, the First-order necessary optimality conditions and the Second-order sufficient optimality condition.
     首先在前人研究的基础上,本文研究了Burgers方程最优控制的一些性质,包括给出J和e的F导数,证明了正则点条件,一阶必要最优条件和二阶充分最优条件。
短句来源
     Furthermor, we consider their nondiferentiable situation, we define nonsmooth univex functions for Lipschitz functions by using Clarke generalized directional derivative and study nonsmooth multiobjective fractional programming with the new convexity. We establish generalized Karush-Kuhn-Tucker necessary and sufficient optimality condition and prove weak, strong and strict converse duality theorems for nonsmooth multiobjective fractional programming problems containing univex functions.
     而且,本文利用Clarke广义方向导数针对Lipschitz函数在原来一致凸函数概念的基础上定义了不可微的一致凸函数,并利用这类新凸性,我们研究了非光滑多目标分式规划,获得了广义Karush-Kuhn-Tucher最优性条件; 弱对偶定理、强对偶定理和严格逆对偶定理。
短句来源
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  sufficient optimality condition
By using these concepts, second-order necessary optimality conditions and a sufficient optimality condition are given in set optimization.
      
A Proof of the Necessity of Linear Independence Condition and Strong Second-Order Sufficient Optimality Condition for Lipschitzi
      
We show that a vector variational inequality is a necessary and sufficient optimality condition for an efficient solution of the vector pseudolinear optimization problem.
      
Furthermore, under appropriate conditions, a necessary optimality condition of the Slater type and a sufficient optimality condition are obtained for a nonsmooth programming problem involving B-vex functions.
      
As applications, we demonstrate that, under invex-convexlikeness assumptions, the Pontryagin maximum principle is a sufficient optimality condition for cooperative differential games.
      
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It is assumed that functions in mathematical programs arc continuously differentiable and have Lipschitzian continuous gradient functions . By use of Clarke's generalized Jacobian matrix, the second -order efficient optimality condition, second-order sufficient optimality condition of minimizing solution for nonlinear programs , and the Lipschitzian continuous property of local minimizing solution for nonlinear parametric programs are given . Then the chief results of Wang Jinde and Fiacco are extended...

It is assumed that functions in mathematical programs arc continuously differentiable and have Lipschitzian continuous gradient functions . By use of Clarke's generalized Jacobian matrix, the second -order efficient optimality condition, second-order sufficient optimality condition of minimizing solution for nonlinear programs , and the Lipschitzian continuous property of local minimizing solution for nonlinear parametric programs are given . Then the chief results of Wang Jinde and Fiacco are extended .

假定所讨论的数学规划问题其函数连续可微且有Lipschitz连续的梯度函数运用Clarke广义Jacobi矩阵,给出了非线性规划(NLP)问题解的二阶最优性必要条件二阶最优性充分条件及非线性参数规划问题解的Lipschitz连续性质,推广了王金德Fiacco的主要结果。

n the nonlinear programming,one of more sucussful methods where a constrained nonlinear pvogramnving problem is transformed into a single unconstrained problem or into a finite sequence of unconstrained problem is the exact penalty function method,which was put forward by Zangwill and its existence was confosimed under suitable assumptions. Up to1970's, this method was considered and mentioned in many popers,The paper [1] is one ofthe most in pressine. On the basis of its main vesult,the kuhn-Tuches second...

n the nonlinear programming,one of more sucussful methods where a constrained nonlinear pvogramnving problem is transformed into a single unconstrained problem or into a finite sequence of unconstrained problem is the exact penalty function method,which was put forward by Zangwill and its existence was confosimed under suitable assumptions. Up to1970's, this method was considered and mentioned in many popers,The paper [1] is one ofthe most in pressine. On the basis of its main vesult,the kuhn-Tuches second order sufficient optimality condition implies the existence of exact iceal penalty functions under convexity of the penalty term In this paper, we develop this theory constantly, increase a constrained condition x∈X and omit convexity of the penalty term Q,tinally,we obtain sesult ofsimilar the paper [1].

在非线性规划中,把约束最优化问题化为无约束最优化问题一个较成功的方法之一就是精确罚函数法。它最早由Zangwill提出,并在一定的条件下证明了它的存在性。到七十年代,这一方法就得到了很大的重视,并出现了许多有关文献.文献[1]就是其中很有影响的文献之一。根据其的主要结论所证明的若惩罚项Q是凸函数,则K-T二阶充分条件可以保证局部精确罚函数存在,对此继续作了进一步推广,增加了约束条件x∈X,并且去掉了Q的凸性假设,对于这种更一般的模型,同样证明了文献[1]中的相应结论。

For set valued vector minimization problem with inequality constraint, a sufficient optimality condition theorem and a necessary Fritz John type optimality condition theorem is derived in terms of the generalized contingent epiderivative. Finally,a Kuhn Tucker necessary type optimality condition theorem for the set valued vector minimization problem is presented in terms of contingent epiderivative.

用广义相依上导数 ,描述了含不等式约束的集值向量极小化问题的最优性充分条件与Fritz John型最优性必要条件。最后还用相依上导数描述了该集值极小化问题的Kuhn Tucker型最优性必要条件。

 
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