梯度法

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。

In inner loop,we use a modified conjugate gradient algorithm and a restarted technique; in outer loop, the Morozov's discrepancy principle is used as a stopping rule.

该方法的内层循环采用修改的共轭梯度法，并使用重开始技巧；外层循环使用Morozov偏差准则作为停机准则。

Conjugate gradient methods are very important for solving nonlinear optimization problems.

共轭梯度法是解决无约束非线性最优化问题的重要的方法之一。

A surrogate subgradient with penalty function method is also used to solve unit commitment.

针对以上两点，分别提出了带惩罚项的伪次梯度法和启发式方法解决经济调度问题的两种新方法。

Taking range as the performance function, considering end velocity, height and trajectory slope angle constraints, the optimal glide trajectory was solved by maximum principle of Pontryagin and conjugate-gradient method.

建立了滑翔弹道模型，以射程为指标函数，考虑终端速度、高度和弹道倾角约束，采用庞特里亚金极大值原理和共轭梯度法求出控制变量有约束的最优滑翔弹道，简要分析了滑翔增程机理。

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。

The philosophy of General Reduced Gradient method is applied to conventional GeneticAlgorithm and a new Hybrid Genetic Algorithm is proposed.

将广义简约梯度法思想应用于传统遗传算法，提出一种新的混合式遗传算法，此方法具有很强的全局和局部搜索能力，并且无需复杂的编码、解码过程，可以准确解决多变量、多峰值的给水管网现状分析问题。

First of all, on the base of the reduced gradient method of Wolfe, we added accurate one dimension searching method into it and gained a new algorithm (algorithm 1,2) for the nonlinear programming with linear equality constraints and quadratic programming problems, and proved convergence of algorithm, then, we use above algo...

首先本文在Wolfe既约梯度法的基础上，针对具有线性等式约束的非线性规划问题和二次规划问题，引入了精确的一维搜索，得到了带一维搜索的新算法(算法1、2)，并给出了算法的收敛性证明。

The philosophy of General Reduced Gradient method is applied to conventional GeneticAlgorithm and a new Hybrid Genetic Algorithm is proposed. Tl1is Il1ethod has a powerful searchingability globally and locally, with which the issues in analyzing the current statlls of water distribution networksfeaturing more variables and more peak values can be solved accurately without any complicated coding and de-coding processes.

将广义简约梯度法思想应用于传统遗传算法，提出一种新的混合式遗传算法，此方法具有很强的全局和局部搜索能力，并且无需复杂的编码、解码过程，可以准确解决多变量、多峰值的给水管网现状分析问题。

The results show that the depths calculated by the vertical grads method are quite satis factory under various conditions.

在具有高分辨率资料的情况下，垂向梯度法是4种方法中计算东海夏季跃层上界深度的最佳方法。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。