| 1. | The smaller the value of the merit function is , the closer the iteration point is to the solution
当价值函数的值越小时，迭代点越靠近最优解。 |
| 2. | This algorithm allows the search direction with only moderate accuracy , and does not require the feasibility of the iteration points
该算法允许搜索方向有相对较大的误差，且不要求迭代点的可行性。 |
| 3. | The main task of traditional methods is to construct iterative points and that of parameter control methods is to find a sequence of parameters
传统算法的关键是构造迭代点，而参数控制算法的关键是构造参数序列。 |
| 4. | Without the strict feasibility of the initial points and iteration points , the algorithm is shown to possess both polynomial - time complexity and q - linear convergence
该算法不要求初始点及迭代点的可行性且具有q -线性收敛速度和多项式时间复杂性。 |
| 5. | The basic idea is to find iterative points which converge to optimal point and its corresponding objective function or merit function values converge to optimal value
其基本思想是构造迭代点来逐步逼近最优点，相应的目标函数值或评价函数值逼近最优值。 |
| 6. | The set of parameters is updated by using the information of the last iteration and brings about the centering effect towards the central path , which was called the self - adjusting effect
这组参数利用上一个迭代点的信息对当前步向中心路径进行调整，文中称之为自调整作用。 |
| 7. | The parameter control methods are in the contrast , which is to find a sequence of parameters that converge to optimal value and its corresponding points in converge to optimal solution
参数控制算法的基本思想正好相反，它是构造参数序列来逼近最优值，相应的迭代点列逼近最优点。 |
| 8. | Of course , the prerequisite for being able to making this shift is that although the trial step is unacceptable as next iterative point , it should provide a direction of sufficient descent
当由信赖域子问题求得的搜索方向不被接受时，利用线搜技术得到接受步长，定义新的有足够下降量的迭代点。 |
| 9. | We use a scaling matrix which make the algorithm generate sequences of point in trust region and the interior of the feasible set . because of the boundedness of the trust region , trust region algorithm can use non - convex approximate models
构造合理的仿射变换矩阵，在投影空间构造信赖域子问题，产生迭代方向，使迭代点既保持在信赖域内，又是严格可行域的内点。 |
| 10. | In general trust region method , a trial point is accepted as a new iterate and the procedure is repeated if the true reduction achieved by the objective function at this point is comparable with the reduction predicted by the quadratic model
考虑到在一般的信赖域方法中，当目标函数沿该搜索方向的实际下降量和预计下降量拟合得比较好时，则由该搜索方向得到新的迭代点并调整信赖域半径。 |
