On a class of nonconvex equilibrium problems

摘要

In this paper, we introduce a new class of equilibrium problems, known as nonconvex equilibrium problems. We suggest some algorithms for solving nonconvex equilibrium problems by using the auxiliary principle technique. The convergence of the proposed methods either requires partially relaxed strongly monotonicity or pseudomononicity. We also introduce the concept of well-posedness for the nonconvex equilibrium problems. As special cases, we obtain a number of known and new results for solving various classes of equilibrium and variational inequality problems. Our results can be considered a significant improvement of the previously known results.