In case of problems with thousands of variables, the primal-dual algorithm will be far more efficient.
对于有大量变量的问题，原始对偶算法将更为有效。
A fast dual algorithm is presented for the piecewise linear programming with successively increasing slopes.
针对目标函数具有递增斜率的分段线性规划问题，提出了一种快速的对偶算法。
Chapter 3 is devoted to the study of the convergence theory of a dual algorithm for unconstrained minimax problems.
第3章给出无约束极大极小问题的一个对偶算法的收敛理论。
This paper analyzes the kernel matrix in the linear programming problem and proposes a new revised prime-dual algorithm based on the kernel matrix.
本文通过对线性规划问题中的核心矩阵的分析，提出了一种基于核心矩阵的原始对偶算法。
Detailed convergence results for the dual algorithm are given and it is proved that there exists a threshold, and the algorithm will converge if the penalty parameter is less than the threshold.
对这一算法给出了精细的收敛性结果，证明了存在罚参数的一个阈值，当罚参数小于这个阈值时，算法收敛。
Detailed convergence results for the dual algorithm are given and it is proved that there exists a threshold, and the algorithm will converge if the penalty parameter is less than the threshold.
对这一算法给出了精细的收敛性结果，证明了存在罚参数的一个阈值，当罚参数小于这个阈值时，算法收敛。
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