Multi-dimensional Variational Control Problem with Data Uncertainty in Objective Functional

Abstract

AbstractThe multi-dimensional optimization model provides the mathematical framework which deals with applied science and engineering, especially in mechanical engineering, due to the fact that the curvilinear integral objective functionals have a physical meaning of mechanical work. The literature on various types of multi-dimensional optimization problems is very rich, which plays a versatile role in mathematics, economics and engineering sciences. Remarkable research works have been achieved toward the multi-dimensional optimization problems by several authors under suitable assumptions. Mititelu [1] obtained the optimality conditions for the multi-dimensional optimization problem and then derived the duality results for it. Treanţă and Arana-Jiménez [2] also studied the multi-dimensional optimization problem under KT-pseudoinvexity assumptions. Further, Treanţă [3] extended his study under the generalized V-KT-pseudoinvexity on the multi-dimensional control problem. Jayswal and Preeti [4] studied the multi-dimensional control problem involving first-order PDE constraints with the help of saddle-point criteria. Then, Jayswal et al. [5] extended the multi-dimensional control problem involving first-order PDE constrained under uncertain data and showed that the constraints problem and its associated penalized problem attain their optimality at the same point under convexity assumptions.