| 1. | Here s the relevant portion from the original
这里是原始问题陈述的相应部分： |
| 2. | Original problem statement
原始问题陈述 |
| 3. | In chapter 3 , we discuss the method for solving nonlinear complementarity problems with the equivalent formulation of equation
第三章，我们考虑了利用原始问题方程形式的等价变形，来解决非线性互补问题的方法。 |
| 4. | In this method , we get the optimal value of semidefinite programming by finding the optimal descent direction of its dual problem
该方法根据次微分理论与半定规划的强对偶定理，通过求解对偶问题得到原始问题的最优值。 |
| 5. | Therefore , our study is very important on the theoretical and practical aspects of svms . the main works in this paper are as follows : 1
在作为支持向量机基础的原始问题解和对偶问题解的关系上，当时研究存在逻辑缺陷。 |
| 6. | An approach to solving a mathematical problem that involves solving a sequence of problem with different parameters ; the parameters are selected so that ultimately the original problem is solved
一种涉及一组具有不同参数的数学问题求解方法，这些参数的选择使得原始问题最终是可求解的。 |
| 7. | Then a suboptimal solution of the graph maximum equal - cut problem is presented employing the randomized algorithm and the improved coordinate ascent ( descent ) algorithm on the optimal solution of semidefmite relaxation
在利用lagrange乘子理论得出原始问题的等价形式之后，将近似算法与改进的坐标上升(下降)算法结合，求得原问题的次优解。 |
| 8. | The quasi - physical method makes the original problem an optimization problem in mathematics . there is often the possibility of going to a local minimum of object function when we solve the optimization problem mathematically . as for how to jump out of the trap of local minimum so that the calculation can head for a region with better prospects , the quasi - physical method is helpless
拟物方法将原始问题落实为优化问题，而用数学方法在求解优化问题时，常常会碰到计算落入目标函数的局部极小值陷阶的困境，如何从这种困境中逃逸出来，使得计算奔向前景更好的区域，拟物方法则无能为力，而应用拟人方法则可以设计出好的“跳出陷阱”策略。 |
| 9. | Executing the lifting method to the equivalent programming , we present a strengthened semidefmite relaxation . as predicted by theory and confirmed by numerical experiments the tight semidefinite relaxation gives a better lower bound of circuit bisection than the one that the previous semidefinite relaxation gives
本文先通过增加非线性约束得到原始问题的等价模型，进而对等价模型利用提升技术，提出了一个强化的半定松弛模型；最后，将结果推广到更具一般性的图的分割问题。 |
| 10. | Proofs were made that global optimum ( or global pareto optimum ) of the decomposed problem and the original mdo problem are equivalent , and the decomposed problem retains all local optima ( or local pareto optima ) of the original mdo problem . by solving the decomposed problem using coevolutionary algorithms , the revolutionary mdo algorithms were formed
证明了用这种分解方式分解后的问题与mdo原始问题的全局最优解(或全局pareto最优解)的等价性，以及这种分解方式保留了mdo原始问题的所有局部最优解(或局部pareto最优解) 。 |
