This article concerns an optimal control problem arising in neo-classical macro-economics, where the objective is to maximize expenditure on social programs over the time horizon by choosing the appropriate balance between investment for growth and consumption. The underlying model and utility function are due to Solow and have their origins in a planning problem studied by Ramsey. The problem is of control theoretic interest, because the right side of the controlled differential equation and also the utility integrand are not uniformly Lipschitz continuous with respect to the state variable, owing to the presence of a fractional singularity. We introduce and apply a nonstandard verification technique, the verification function for which has infinite slope at a point approaching the boundary of its domain, to deal with these singularities and to provide a detailed solution to the problem and analyze its structure, for arbitrary initial data.

中文翻译：

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增长/消费模型的最优控制

本文关注新古典宏观经济学中出现的最优控制问题，其目标是通过选择增长投资和消费之间的适当平衡，在时间范围内最大化社会项目的支出。底层模型和效用函数源于 Solow，起源于 Ramsey 研究的规划问题。该问题具有控制理论的兴趣，因为受控微分方程的右侧以及效用被积函数相对于状态变量不是一致的 Lipschitz 连续的，这是由于存在分数奇点。我们引入并应用了一种非标准验证技术，其验证函数在接近其域边界的点处具有无限斜率，