On Lipschitz continuity of approximate solutions to set-valued equilibrium problems via nonlinear scalarization
Lâm Quốc Anh, Tran Ngoc Tam, Nguyen Huu Danh · Optimization · 2021
In this paper, we consider parametric set-valued equilibrium problems in normed spaces. By virtue of the Gerstewitz nonlinear scalarization function along with relaxed concavity assumptions, we obtain the Lipschitz continuity property of solution maps to such problems. The treatment and obtained results for these problems are new and different from the existing ones in the literature. We apply the main results to the Browder variational inclusion to illustrate for their applicability.