In this paper, we introduce a necessary and sufficient condition of optimality for a new class of multidimensional optimal control problems governed by path‐independent curvilinear integral functionals and mixed constraints involving first‐order partial differential equations (PDEs) of m‐flow type. Furthermore, as a consequence, we establish the equivalence between the class of (strongly) b‐invex functionals and the class of (strongly) b‐pseudoinvex functionals. The mathematical development in the paper is supported by illustrative examples, as well.

中文翻译：

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一类多维控制问题最优性的充要条件

在本文中，我们为一类新的多维最优控制问题引入了最优的充要条件，该最优最优控制问题由与路径无关的曲线积分函数和涉及m流类型一阶偏微分方程（PDE）的混合约束控制。此外，因此，我们建立了（强烈）b伪凸函数的类和（强烈）b伪凸函数类的等价关系。本文中的数学发展也得到了说明性例子的支持。