Robust optimality in constrained optimization problems with application in mechanics

Abstract

This paper deals with necessary and sufficient conditions of optimality for a new robust optimization problem involving curvilinear integral (mechanical work) functionals, which are independent of the path and are determined by uncertain multi-dimensional controlled Lagrangians of second order. More precisely, by using the notion of convex curvilinear integral, provided by uncertain complete integrable controlled Lagrange 1-form, and the concept of robust weak optimal solution to the problem under study, we build a new math context to state the optimality conditions which are necessary and sufficient for a point to be an extreme of the new studied class of robust optimization problems with uncertainty in the constraint and objective functionals. Also, we introduce the concept of a robust Kuhn-Tucker point and establish a characterization result. Moreover, we present a non-trivial illustrative example to validate the results established in the paper.