In this paper, we propose an iterative algorithm to find the optimal incentive mechanism for the principal-agent problem under moral hazard where the number of agent action profiles is infinite, and where there are an infinite number of results that can be observed by the principal. This principal-agent problem has an infinite number of incentive-compatibility constraints, and we transform it into an optimization problem with an infinite number of constraints called a semi-infinite programming problem. We then propose an exterior penalty function method to find the optimal solution to this semi-infinite programming and illustrate the convergence of this algorithm. By analyzing the optimal solution obtained by the proposed penalty function method, we can obtain the optimal incentive mechanism for the principal-agent problem with an infinite number of incentive-compatibility constraints under moral hazard.

在本文中，我们提出了一种迭代算法来寻找道德风险下委托代理问题的最佳激励机制，其中代理行为配置文件的数量是无限的，并且委托人可以观察到无限数量的结果。 . 这个委托代理问题有无数个激励相容约束，我们将它转​​化为一个有无数个约束的优化问题，称为半无限规划问题。然后，我们提出了一种外部惩罚函数方法来找到这种半无限规划的最优解，并说明该算法的收敛性。通过分析提出的惩罚函数方法得到的最优解，