线性规划的表面移动方法
Surface Movement Method for Linear Programming
AI总结：
本文提出线性规划的表面移动方法，在可行多面体表面构建最优目标路径，并用前馈深度神经网络确定移动方向，证明了算法收敛性。
摘要：
本文提出了一种新的线性规划方法，称为表面移动方法。该方法在可行多面体的表面上，从初始边界点构建一条最优目标路径，直至达到目标函数最优值的点。路径的最优性意味着沿目标函数值最大增加/减少的方向移动。文中描述了实现表面移动方法的算法的形式化描述，并证明了该算法的收敛定理。所提出的方法可以通过使用前馈深度神经网络来有效实现，以确定沿可行多面体面的最优移动方向。为此，在当前近似点处构建线性规划问题的多维局部图像。该图像被输入到深度神经网络，网络返回一个向量，该向量确定多面体表面上最优目标路径的方向。
英文摘要：
The article presents a new method of linear programming, called the surface movement method. This method constructs an optimal objective path on the surface of the feasible polytope from the initial boundary point to the point at which the optimal value of the objective function is achieved. The optimality of the path means moving in the direction of maximum increase/decrease in the value of the objective function. A formal description of the algorithm implementing the surface movement method is described. The convergence theorem of this algorithm is proved. The presented method can be effectively implemented using a feed forward deep neural network to determine the optimal direction of movement along the faces of the feasible polytope. To do this, a multidimensional local image of the linear programming problem is constructed at the point of the current approximation. This image is fed to the input of the deep neural network, which returns a vector determining the direction of the optimal objective path on the polytope surface.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
