Non-convex optimal control problems occurring in, e.g., water or power systems, typically involve a large number of variables related through nonlinear equality constraints. The ideal goal is to find a globally optimal solution, and numerical experience indicates that algorithms aiming for Karush-Kuhn-Tucker points often find (near-)optimal solutions. In our paper, we provide a theoretical underpinning for this phenomenon, showing that on a broad class of problems the objective can be shown to be an invariantly convex function (invex function) of the control decision variables when state variables are eliminated using implicit function theory. In this way, near-global optimality can be demonstrated, where the exact nature of the global optimality guarantee depends on the position of the solution within the feasible set. In a numerical example, we show how high-quality solutions are obtained with local search for a river control problem where invexity holds.

中文翻译：

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通过隐藏不变凸性进行模型预测控制的全局最优

发生在例如水或电力系统中的非凸最优控制问题通常涉及通过非线性等式约束相关的大量变量。理想的目标是找到全局最优解，数值经验表明，针对 Karush-Kuhn-Tucker 点的算法经常会找到（接近）最优解。在我们的论文中，我们为这种现象提供了理论基础，表明在使用隐函数理论消除状态变量时，在广泛的问题类别中，目标可以显示为控制决策变量的不变凸函数（凸函数） . 通过这种方式，可以证明近全局最优性，其中全局最优性保证的确切性质取决于可行集中解的位置。在一个数值例子中，