Optimality in constrained fractional robust optimization problems

This paper presents conditions that are both necessary and sufficient for optimal solutions in a new robust fractional optimization problem defined by continuous curvilinear integral derived from uncertain high-dimensional controlled Lagrangeans. We employ the concept of a convex curvilinear integral, defined through an integrable controlled Lagrangean, in conjunction with the notion of a robust weak optimal solution. This theoretical framework enables the establishment of optimality conditions necessary for identifying extreme solutions in a new category of robust optimization problems characterized by variability in both the constraints and the performance criteria. Furthermore, we present the concept of a robust Kuhn–Tucker point and offer a description result. To substantiate our theoretical contributions, we include an illustrative example.