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Continuity of Solution Maps to Parametric Set Optimization Problems via Parametric Equilibrium Problems
Lam Quoc Anh
,
Nguyen Huu Danh
,
Tran Ngoc Tam
Abstract
In this paper, we consider set optimization problems with respect to set less order relations. We introduce nonlinear scalarization functions for sets and study several properties of such functions. Using the concerning functions, we investigate relationships between set optimization problems and equilibrium problems. Sufficient conditions for the continuity of solution maps to such problems via equilibrium problems are established.