| 1. | Dual problem and sensitivity analysis of linear programming
线性规划对偶问题及其灵敏度分析 |
| 2. | Constraint qualifications and dual problems for quasi - differentiable programming
拟可微规划的约束规范和对偶问题 |
| 3. | Discussion on the conversion methods of problem and dual problem in linear programming
线性规划中原问题与对偶问题转化方法探讨 |
| 4. | Simple and convenient implementation of solution and sensitivity analysis of linear programming and dual problem with excel
上轻松实现线性规划及其对偶问题的求解以及灵敏度分析 |
| 5. | 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。 |
| 6. | In chapter six we consider the dual problem , develop several computational procedures based on duality , and discuss sensitivity and parametric analysis
在第六章中，我们考虑对偶问题，基于对偶建立几个计算程序，并讨论了参数和灵敏度分析。 |
| 7. | We show that the hybrid method is globally and superlinearly convergent for nonzero residual problems and globally and quadratically for zero resi dual problems
因此，该杂交方法对于零残量问题是二阶收敛的，而对于非零残量问题是超线性收敛的。 |
| 8. | Dual mathematical programming is used to map the original problem exactly and the second approximation of the dual problem is set up by taylor ' s expand form , it is solved by qp ( quadratic programming ) solving device
用对偶数学规划精确映射原问题，用泰勒展式建立对偶问题的二阶近似。最后用二次规划求解器求解。 |
| 9. | Abstract : in this paper , we propose an improved lagrangian relaxation algorithm to solve job - shop scheduling problems . besides the addition of augmented objective , we expand the search scope of near - optimal solutions and improve the computational efficiency greatly by restricting the solution scope of sub - problems and modifying the search method of dual problem . at the same time , we develop a genetic algorithm combining with the lr ( lagrangian relaxation ) method . using the numerous useful solutions we get in the lagrangian relaxation as the original genes , we can improve the solution further . test results show that these methods achieve satisfied outcome for job - shop problems . they can also be applyed to other programming problems with constraints
文摘:针对车间调度问题，提出了一种改进的拉氏松弛算法.在增加辅助目标函数的基础上，通过对子问题的限制和搜索策略的改变，使拉氏算法的计算量减少，近优解的搜索能力有很大改善.本文还提出了一种基因优化算法，充分利用拉氏算法得到的多个近优解，进一步优化结果.仿真结果表明对车间调度问题得到了较好的结果.本方法也可用于其它有约束的规划问题 |
| 10. | According to the dual theory , a simple geometric programming was proposed to derive a corresponding geometric dual problem instead of cross - entropy optimization problem with cross - entropy constrains , which is a concave programming one with linear constrains , leading to a simpler calculation
根据对偶理论，提出了一个简单的几何规划，该方法把一个带有叉熵约束的叉熵优化问题转化成了一个对偶规划，而对偶规划是一个只需要解决一个带有线性约束的凸规划问题，比较容易计算。 |
