Abstract. This paper is devoted to the investigation of robust -optimal solution sets for convex optimization problems with data uncertainty in both the objective and constraints. We first establish some properties of the Lagrangian-type function corresponding to a multiplier associated to the given robust -optimal solution. Then, we describe a new approach to characterize the robust -optimal solution sets of this uncertain convex optimization problem via the study of the relationships among the set of Lagrange multipliers corresponding to robust -optimal solutions, the set of -Kuhn-Tucker vectors, and the set of robust -optimal solutions of its Lagrangian dual problem.
How to Cite this Article:
X. Guo, Y. Zhang, X. Sun, Characterizing robust -optimal solution sets for uncertain convex optimization problems, J. Nonlinear Var. Anal. 9 (2025), 423-433.
