Journal of Nonlinear and Variational Analysis

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DOI: 10.23952/jnva.11.2027.1.05

Volume 11, Issue 1, 1 February 2027, Pages 77-114

 

Abstract. In this paper, we unify the lower and upper semicontinuity of a set-valued map and apply this to analyze the qualitative properties of weakly efficient and efficient solutions in set optimization problems. Our approach involves a proposed unification of the set less relation based on the Minkowski difference, including existence and stability conditions. First, we unify the upper and lower semicontinuity of a set-valued map and discuss its properties and characterizations. Next, building on these ideas, we propose a unification of the set less relations via the Minkowski difference and examine its properties. Then, we observe that the unification of semicontinuity is highly compatible with the unified form of these set relations in studying the qualitative properties of set optimization problems. Furthermore, in analyzing these solution properties, we introduce new approaches that allow us to establish stability conditions for set optimization problems without relying on coercive conditions, as required in previous works. To demonstrate the practical relevance of the results obtained, we further employ them to analyze the convergence behavior of interval optimal control problems and the irrigation management model under uncertainties in rainfall and cost.

 

How to Cite this Article:
L.Q. Anh, L.V. Day, L.T.V. Khanh, X. Zhao, Unification of semicontinuities and applications in analyzing stability for set optimization problems, J. Nonlinear Var. Anal. 11 (2027), 77-114.