Duality Results for a Class of Constrained Robust Nonlinear Optimization Problems

In this paper, we establish various results of duality for a new class of constrained robust nonlinear optimization problems. For this new class of problems, involving functionals of (path-independent) curvilinear integral type and mixed constraints governed by partial derivatives of second order and uncertain data, we formulate and study Wolfe, Mond-Weir and mixed type robust dual optimization problems. In this regard, by considering the concept of convex curvilinear integral vector functional, determined by controlled second-order Lagrangians including uncertain data, and the notion of robust weak efficient solution associated with the considered problem, we create a new mathematical context to state and prove the duality theorems. Furthermore, an illustrative application is presented.