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 sufficient descent condition 充分下降条件(5)充分下降性(5)
 充分下降条件
 1. A mixed HS-FR conjugate gradient algorithm is proposed. Two convergence theorems without the sufficient descent condition for the mixed HS-FR algorithm are given. 1．给出了一个混合的HS-FR共轭梯度算法，在无充分下降条件下，得到了关于HS-FR算法的两个收敛性定理。 短句来源 A new nonlinear conjugate gradient formula for solving unconstrained optimization problem is proposed. The formula satisfies the sufficient descent condition,and the method in which the proposed formula and the weak Wolfe conditions are used is global convergence. 提出一个新的解决无约束最优化问题的非线性共轭梯度公式,该公式满足充分下降条件,采用这个公式和弱W olfe条件的方法是全局收敛的. 短句来源 Global convergence analysis without the sufficient descent condition of the method is given. 第二章对一类非单调的共轭梯度算法进行了研究，在没有充分下降条件的情况下，建立了全局收敛性结果。 短句来源 In chapter 4, we will try to promote this line search to other conjugate gradient methods without the sufficient descent condition. 在第四章中我们试图将在无需充分下降条件的前提下把这种线搜索推广到其它的共轭梯度法中去。 短句来源 The distinguishing feature of the new method is that it satisfies sufficient descent condition naturally. Its global convergence is proved when F is P_0 + R_0 and quadratic continuous differentiate function. Numerical results are given which indicate that the method is efficient. 此算法的突出特点是自然满足充分下降条件，在F是P_0+R_0的二次连续可微函数时，证明了算法的全局收敛性，文后的数值实验表明该算法具有潜力。 短句来源
 充分下降性
 The first method is modified by the method which satisfies the sufficient descent condition under Powell's restart rule and the standard Armijo line search. 对第一个共轭梯度法进行修正，使得修正后的方法在Powell再开始准则及标准的Armijo线性搜索条件下满足充分下降性条件。 短句来源 In Chapter 2, we propose a new kind of conjugate gradient-type formula for solving nonlinear unconstrained optimization problems, the new method definds the range of paremeters by using the famous foumula β_k~(CD) which expands the range of parameters comparing with the old method, and we have proved the new formula satisfies the sufficient descent condition and the corresponding algorithm with general Wolfe line search possesses the global convergence result. 第二章，给出了一类求解非线性无约束优化问题的新的共轭梯度类型公式，新公式借助著名公式β_κ~(CD)来定义参数的取值范围，和原来的公式比较新公式不但扩大了参数的取值范围，且仍具有充分下降性，相应算法在广义Wolfe线搜索下具有全局收敛性。 短句来源 In Chapter 3, a new nonlinear conjugate gradient formula for solving unconstrained optimization problem is proposed, which is constructed by combining the famous formula β_k~(FR) with β_k~(PRP), the new formula satisfies the sufficient descent condition, and the corresponding algorithm under the weak Wolfe condition is global convergent. 第三章，提出了求解无约束优化问题的另一种新的共轭梯度公式，该公式是把著名公式β_κ~(FR)和β_κ~(PRP)有效结合起来构成的，新公式具有充分下降性，并且相应算法在弱Wolfe条件下具有全局收敛性。 短句来源 This formula with non-negative values possesses some favorable properties: (1) the sufficient descent condition holds without any line searches; 本文证明了这一新的公式在限制其值是非负的条件下具有如下性质：(1)不需要任何线搜索可以保持充分下降性； 短句来源 A new nonlinear conjugate gradient type formula for solving unconstrained optimization problems is proposed, the corresponding method satisfies the sufficient descent condition when Powell's restart criterion is used. 给出了一个求解非线性无约束优化问题的新的共轭梯度类型公式,并证明了相应的方法在Powell再开始准则下具有充分下降性. 短句来源
 “sufficient descent condition”译为未确定词的双语例句
 The CD method can ensure all descent search directions satisfy the sufficient descent condition. 而且在这两种Armijo型线搜索下得到CD法的全局收敛性结果。 短句来源 A new nonlinear conjugate type formula for solving unconstrained optimization problems is proposed,the corresponding method satisfies the sufficient descent condition in the condition of strong wolfe steplength rule and Powell's restart criterion,furthermore,the method converges globally under some conditions. 提出一种求解无约束问题的新的共轭梯度类型公式,与此相应的方法在强Wolfe线搜索和Powell再开始条件下满足下降条件,并且在适当的情况下具有全局收敛性质. 短句来源

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 In this paper, the global convergence properties of conjugate gradient methods are studied. Under the relax strong Wolfe linesearch, we study the global convergence of HS method by using sufficient descent condition and prove the global convergence of PR conjugate gradient method with Armijo or Goldstein linesearch is also established. Meanwhile the global convergence of a modified HS conjugate gradient method with general Wolfe linesearch without sufficient descent condition is proved. 研究共轭梯度算法的整体收敛性，在放宽了的强Ｗｏｌｆｅ搜索（１８）、（１９）下证明了［１］中提出的修正ＨＳ共轭梯度算法的收敛性，在充分下降性条件下，βｋ＝ｍａｘβＨＳｋ，０｛｝时也具有整体收敛性，同时，βｋ＝ｍａｘ０，βＰＲｋ｛｝时，利用Ａｒｍｉｊｏ搜索和Ｇｏｌｄｓｔｅｉｎ搜索的共轭梯度法也具有整体收敛性． A new nonlinear conjugate type formula for solving unconstrained optimization problems is proposed,the corresponding method satisfies the sufficient descent condition in the condition of strong wolfe steplength rule and Powell's restart criterion,furthermore,the method converges globally under some conditions. 提出一种求解无约束问题的新的共轭梯度类型公式,与此相应的方法在强Wolfe线搜索和Powell再开始条件下满足下降条件,并且在适当的情况下具有全局收敛性质. A new nonlinear conjugate gradient type formula for solving unconstrained optimization problems is proposed, the corresponding method satisfies the sufficient descent condition when Powell's restart criterion is used. The computational result is presented. 给出了一个求解非线性无约束优化问题的新的共轭梯度类型公式,并证明了相应的方法在Powell再开始准则下具有充分下降性.文章最后给出了该方法的数值结果. << 更多相关文摘
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