We consider continuous linear programs over a continuous finite time horizon T , with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions. Specifically, we search for optimal solutions in the space of measures or of functions of bounded variation. These models generalize the separated continuous linear programming models and their various duals, as formulated in the past by Anderson, by Pullan, and by Weiss. In previous papers we formulated a symmetric dual and have shown strong duality. We also have presented a detailed description of optimal solutions and have defined a combinatorial analogue to basic solutions of standard LP. In this paper we present an algorithm which solves this class of problems in a finite bounded number of steps, using an analogue of the simplex method, in the space of measures.

中文翻译：

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常系数连续线性规划的单纯形算法

我们考虑在连续有限时间范围 T 上的连续线性程序，具有常数系数矩阵、线性右侧函数和线性成本系数函数。具体来说，我们在度量空间或有界变异函数的空间中寻找最优解。这些模型概括了分离的连续线性规划模型及其各种对偶，正如 Anderson、Pullan 和 Weiss 过去所制定的那样。在之前的论文中，我们制定了一个对称对偶并表现出很强的对偶性。我们还详细描述了最优解，并定义了标准 LP 基本解的组合模拟。在本文中，我们提出了一种算法，该算法使用与单纯形法类似的方法，在有限步数内解决此类问题，