<p>This work aims to investigate the well-posedness properties for set optimization problems involving set less relation via the nonlinear scalarization method. Firstly, we propose concepts of cone-outer and cone-inner semicontinuities of a set-valued mapping and discuss their properties. Next, we employ these results to study the lower semicontinuity of nonlinear scalarization functions concerning the set less relation. After that, we suggest notions of pointwise and global well-posedness for set optimization problems via the set less relation, and then, by using these scalarization functions, we consider relationships between well-posedness properties of set optimization problems and that of scalar ones. Finally, sufficient conditions for both pointwise and global well-posedness of set optimization problems are obtained by employing results of the scalar problems.</p>