再进一步通过非线性规划的对偶理论把原问题（一定量的化肥产出最多的粮食）转化为对偶问题（dual problem）,即要产出一定量的粮食，至少需要多少化肥。
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quadratic dual problem [数] 二次对偶问题
wolfe dual problem wolfe对偶
dual problem of convex programming 凸规划对偶问题
dual problem of nonlinear programming 非线性规划对偶问题
dual linear programming problem 对偶线性规划问题
The sub-gradient algorithm is designed to solve lagrangian dual problem according to its characteristic. In computational example, the result of contrastive test shows the algorithm effectiveness.
根据问题的特性设计了次梯度算法求解拉格朗日对偶问题。
参考来源 - 不确定性条件下供应链管理优化模型及算法研究In this part the deducing process of the optimality condition of SVM dual problem and the proof to the convergence of SMO are also given.
本部分还分析了SMO算法的收敛性,首先推导SVM对偶问题的最优性条件,进而证明了SMO算法的收敛性定理。
参考来源 - 支持向量机的算法研究·2,447,543篇论文数据，部分数据来源于NoteExpress
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。
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