In this paper, we consider resource allocation problem stated as a convex minimization problem with linear constraints. To solve this problem, we use gradient and accelerated gradient descent applied to the dual problem and prove the convergence rate both for the primal iterates and the dual iterates. We obtain faster convergence rates than the ones known in the literature. We also provide economic interpretation for these two methods. This means that iterations of the algorithms naturally correspond to the process of price and production adjustment in order to obtain the desired production volume in the economy. Overall, we show how these actions of the economic agents lead the whole system to the equilibrium.

在本文中，我们将资源分配问题视为具有线性约束的凸最小化问题。为了解决这个问题，我们将梯度和加速梯度下降应用于对偶问题，并证明原始迭代和对偶迭代的收敛速度。我们获得了比文献中已知的更快的收敛速度。我们还为这两种方法提供了经济解释。这意味着算法的迭代自然对应于价格和产量调整的过程，以获得经济中所需的产量。总的来说，我们展示了经济主体的这些行为如何引导整个系统达到平衡。