Robust duality for nonconvex uncertain vector optimization via a general scalarization

This paper concentrates on robust duality relations for uncertain cone-constrained vector optimization problems in more general nonconvex settings. First, different from the existing results, a new class of generalized Lagrange functions of the considered problem is introduced by combining the image space analysis method and scalarization technique. Then, the Lagrange robust vector dual problem is formulated. Subsequently, the results of robust weak duality, strong duality and converse duality are given respectively, which characterize vector dual relations between the primal worst and dual best problems. Simultaneously, some examples are given to illustrate our results.

Automated summary

This paper focuses on the robust duality relations for uncertain cone-constrained vector optimization problems in more general nonconvex settings. The authors introduce a new class of generalized Lagrange functions by combining the image space analysis method and scalarization technique, and formulate the Lagrange robust vector dual problem. The results of robust weak duality, strong duality, and converse duality are provided to characterize the vector dual relations between the primal worst and dual best problems.