Nonlinear Separation and Saddle Points for Quasi-EquilibriumProblems with Cone Constraints

A new generalized nonlinear separation scheme of quasi-equilibrium problems with cone constraints was established by the image space analysis method, and the Lagrangian saddle point conditions and optimality conditions of quasi-equilibrium problems with cone constraints are examined. Under suitable conditions, the equivalence of the Lagrangian saddle point conditions and optimality conditions of quasi-equilibrium problems with cone constraints are proven to be equivalent