Hadamard well‐posedness for a set‐valued optimization problem

In this paper, we introduce a kind of Hadamard well‐posedness for a set‐valued optimization problem. By virtue of a scalarization function, we obtain some relationships between weak $(\epsilon ,e)$ ‐minimizers of the set‐valued optimization problem and $\epsilon$ ‐approximate solutions of a scalar optimization problem. Then, we establish a scalarization theorem of P.K. convergence for sequences of set‐valued mappings. Based on these results, we also derive a sufficient condition of Hadamard well‐posedness for the set‐valued optimization problem.