The maximization problem is then called the primal problem, and the minimization is the dual problem.
在这个意义上最大化问题会被称为初始问题，最小化问题就称为对偶问题。
The paper offers a dual problem for the semi-infinite convex programming by using the directional derivative with zero dual gap.
本文对半无限凸规划提出一个用方向导数表述的对偶问题，其对偶间隙为零。
Analyzes the relation between the generalized moment problem and its dual problem, and gives a new method for solving some generalized moment problems.
分析了随机最优化领域中广义矩问题及其对偶问题的关系，从而提出了广义矩问题的一种新的求解方法。
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。
This paper analyzes the relation between the generalized moment problem and its dual problem, and gives the solution to some generalized moment problems.
分析了广义矩问题及其对偶问题的关系，获得了求解广义矩问题的方法。
According to the dual theory, the dual programming was used to map the original problem exactly and the second approximation of the dual problem was set up by Taylor's expansion.
根据对偶理论，应用对偶规划精确映射原问题，再按泰勒展式建立对偶问题的二阶近似。
A projection subgradient algorithm for the Lagrangian dual problem of the relaxed quadratic problem is employed to general lower bounds of the optimal value for the original problem.
采用椭球剖分策略剖分可行域为小的椭球，用投影次梯度算法解松弛二次规划问题的拉格朗日对偶问题，从而获得原问题的一个下界。
A projection subgradient algorithm for the Lagrangian dual problem of the relaxed quadratic problem is employed to general lower bounds of the optimal value for the original problem.
采用椭球剖分策略剖分可行域为小的椭球，用投影次梯度算法解松弛二次规划问题的拉格朗日对偶问题，从而获得原问题的一个下界。
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