投影梯度法

词组短语

projection gradient method

与投影梯度法相关的网络例句 [注：此内容来源于网络，仅供参考]

Keywords Closed convex cone;gradient projection method;Least-squares solution;Inverse matrix problem;Inverse eigenvalue problem;Matrix completion problem;Optimal approximation

Article From 湖南大学；应用数学博士论文 2005年度闭凸锥；投影梯度法；最小二乘解；矩阵反问题；矩阵逆特征值问题；矩阵完全化；最佳逼近

In this paper, we give a new class of adaptive nonmonotone spectral projected gradient technique for convex constrained optimization.

该文给出了求解凸约束优化的一类新的自适应非单调谱投影梯度法，主要思想是通过引入具有自适应性的权重参数，使算法在迭代过程中能自动调节非单调策略。

In chapter 2 we propose a linear equality constraint optimization question , the new algorithm is combined with the new conjugate gradient method(HS-DY conjugate gradient method)and Rosen"s gradient projection method , and has proven it"s convergence under the Wolfe line search.In chapter 3 we have combined a descent algorithm of constraint question with Rosen"s gradient projection, and proposed a linear equality constraint optimization question"s new algorithm, and proposed a combining algorithm about this algorithm, then we have proven their convergence under the Wolfe line search, and has performed the numerical experimentation.

在第三章中我们将无约束问题的一类下降算法与Rosen投影梯度法相结合，将其推广到线性等式约束最优化问题，提出了线性等式约束最优化问题的一类投影下降算法，并提出了基于这类算法的混合算法，在Wolfe线搜索下证明了这两类算法的收敛性，并通过数值试验验证了算法的有效性。

Rosen projective gradient method is used to find the approximated KKT points of relaxed problem, and then the index set is updated until the minimal solution is .

本文采用Rosen 投影梯度法求此松弛问题的近似KKT点，然后更新指标集不断迭代直至得到最优解。

Then depended on the Gradient Projection Method, the gradient projection direction is deduced. The gradient direction is the basement for sensitivity analysis.

接着，根据投影梯度法，推导出了投影梯度方向，该方向是灵敏度分析的基础。

The projection gradient method will be a possible way to solve the problem that we just get. It has been shown that the projections of the every directions, of which is the boundary point in linear restraint problems, are the possible decent directions, and the projection of negative grads direction is a decent direction. In 1960, Rosen proposed the basic idea of projection gradient methods, and then lots of researchers have been tried to find the convergence of this method. But most of them get the convergence with the condition to amend the convergence itself.

在约束最优化问题的算法中怎样寻找有效的下降方向是构造算法的重要内容，在寻找下降方向方面可行方向法中的投影梯度法有效的解决了下降方向的寻找问题，利用线性约束问题边界点的任意方向在边界上的投影都是可行方向，而负梯度方向的投影就是一个下降方向。60年代初Rosen提出投影梯度法的基本思想，自从Rosen提出该方法以后，对它的收敛性问题不少人进行了研究，但一般都是对算法作出某些修正后才能证明其收敛的，直到最近对Rosen算法本身的收敛性的证明才予以解决。

Until recently, the convergence of the Rosen"s arithmetic has been proved. The projection gradient method is the generalization of Steepest decent method to constraint problem. So it does have a faster convergence speed that the fastest decent method . To solve the problem, many researchers have generalizat the well-developed optimization with unconstraint to the Rosen"s gradient method. The conjugate gradient method is one of success to solve the problem.

投影梯度法是最速下降法对约束问题的推广，因此没有较快的收敛速度，为了解决这个问题很多中外学者把发展得比较成熟的无约束最优化算法作类似的推广，其中共轭梯度方法是近年发展的很成熟的方法，它具有计算简单，算法结构好，计算量少，具有良好的收敛性等优点，而Rosen投影梯度法的提出使寻找下降方向变得简单。

In the optimal control of kinematics for redundant robots, two new concepts, the matrix weightability measure and the self-motion declinability measure are proposed. Further, a modified weighted gradient projection method which combines gradient projection method with weighted least-norm solution is presented, it can attain ideal optimal effects at low velocities.

本文对冗余自由度机器人的运动学、动力学和容错等方面的优化控制进行了深入的分析和探讨：在冗余度机器人运动学优化控制方面，提出矩阵可加权度和自运动可衰度的概念，将梯度投影法和加权最小范数解法有机的相结合，形成可优化能力强、关节速度较低的改进的加权梯度法。

A problem of cable force optimization of cable-stayed bridge is equated as a nonlinear implicit optimization model. In the mathematical model, the object function is minimizing summation of bending strain energy and axial strain energy, and the constrain conditions are nonlinear and related to reasonable finished dead state. The optimization model is solved by projection gradient method, fully considering all kinds geometric nonlinearity.

把超千米级斜拉桥的索力优化问题归结为非线性隐式优化的数学模型，以系统最小弯压应变能为目标，根据合理成桥状态指定各种非线性约束条件，利用投影梯度法进行优化问题的求解，求解过程中充分考虑了各种几何非线性的影响。

In this paper the characters of MA model and the trust region method are analyzed, a subproblem with MA model and trust region technique is presented, and a projected gradient method is use.

本文分析了MA模型和信赖域方法的特点，构造了MA模型信赖域子问题，并利用投影梯度法进行求解，在此基础上提出了一个新的求解非线性规划问题的MA模型信赖域方法。

与投影梯度法相关的网络解释 [注：此内容来源于网络，仅供参考]

axonometric projection method：轴测投影法

共轭梯度:conjugate gradient method | 轴测投影法:axonometric projection method . | 投影类算法:Projection-type method

projection gradient method：投影梯度法

projection 射影 | projection gradient method 投影梯度法 | projection matrix 射影矩阵

orthogonal projection method：正交投影方法

平行投影法:Parallel Projection Method | 正交投影方法:orthogonal projection method | 梯度投影法:gradient projection method

gradient projection method：梯度投影法

梯度算子 gradient operator | 梯度投影法 gradient projection method | 梯度相关法 gradient related method

gradient projection method：梯度投影方法

投影梯度法:Gradient Projection Method | 梯度投影方法:gradient projection method | 柔度投影法:flexibility projection method

gradient projection method：投影梯度法

精化投影方法:refined projection method | 投影梯度法:Gradient Projection Method | 梯度投影方法:gradient projection method

modified gradient projection method：修正梯度投影法

修正单纯形法|revised simplex method | 修正梯度投影法|modified gradient projection method | 需求|demand

modified gradient projection method：修改梯度投影法

修改黄金分割搜索 modified Fibonacci search | 修改梯度投影法 modified gradient projection method | 修改的目标函数 modified objective function

The Gradient Projection Method：投影梯度法

投影算法:Projection method | 投影梯度法:The Gradient Projection Method | 投影类算法:Projection-type method

projection matrix：射影矩阵

projection gradient method 投影梯度法 | projection matrix 射影矩阵 | projection plane 射影平面