经典定价理论认为，市场出清价格应确定为市场优化问题的对偶解。
A clearing price is directly obtained from the dual solution of market optimization in standard pricing.
接着，利用函数的上次微分构造了不可微向量优化问题（VP）的广义对偶模型，并且在适当的弱凸性条件下建立了弱对偶定理。
Finally, the generalized dual model of the problem (VP) is presented with the help of upper subdifferential of function, and a weak duality theorem is given.
然后，运用凸优化技术分析了该资源分配问题，并基于拉格朗日对偶法给出了一种子载波和功率最优分配算法。
Then, by use of multiple carrier system's frequency-sharing property and convex optimization, a subcarrier and power optimal allocation algorithm is proposed based on Lagrangian duality theory.
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。
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。
Analyzes the relation between the generalized moment problem and its dual problem, and gives a new method for solving some generalized moment problems.
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