Generalized Ordered Weighted Aggregation Robustness to Solve Uncertain Single Objective Optimization Problems (2410.03222v1)

Abstract: Robust optimization aims to find optimum points from the collection of points that are feasible for every possible scenario of a given uncertain set. An optimum solution to a robust optimization problem is commonly found by the min-max robust counterpart or by the best out of the worst-cases analysis. In this article, we introduce a new counterpart with the help of the generalized ordered weighted aggregation (GOWA) operator to solve uncertain single objective optimization problems. After introducing GOWA robustness, we analyze a few elementary properties of the GOWA robust objective function, like continuity, monotonicity, coerciveness, local Lipschitz property, and subdifferential regularity. An approach to computing the Clarke subdifferential of the GOWA robust objective function is also provided. We discuss the relationship between the concept of GOWA robustness with other existing robustness -- flimsily, highly, min-max, light, and min-min robustness. We show that in a particular case, GOWA robustness reduces to the commonly used min-max robustness. The entire paper is supported by several geometrical and numerical illustrations.