Convexity and closedness in stable robust duality

The paper deals with optimization problems with uncertain constraints and linear perturbations of the objective function, which are associated with given families of perturbation functions whose dual variable depends on the uncertainty parameters. More in detail, the paper provides characterizations of stable strong robust duality and stable robust duality under convexity and closedness assumptions. The paper also reviews the classical Fenchel duality of the sum of two functions by considering a suitable family of perturbation functions.This research was supported by the Ministry of Economy and Competitiveness of Spain and the European Regional Development Fund (ERDF) of the European Commission, Project MTM2014-59179-C2-1-P, by the Australian Research Council, Project DP160100854, and by Vietnam National University - HCM city, Vietnam, project “Generalized scalar and vector Farkas-type results with applications to optimization theory”