Well-posed generalized vector equilibrium problems

Abstract

In this paper, we establish the bounded rationality model M for generalized vector equilibrium problems by using a nonlinear scalarization technique. By using the model M, we introduce a new well-posedness concept for generalized vector equilibrium problems, which unifies its Hadamard and Levitin-Polyak well-posedness. Furthermore, sufficient conditions for the well-posedness for generalized vector equilibrium problems are given. As an application, sufficient conditions on the well-posedness for generalized equilibrium problems are obtained. MSC: 49K40; 90C31

Generalized Well-Posedness for Symmetric Vector Quasi-Equilibrium Problems

“…By employing the scalarization function, we give some sufficient conditions to guarantee the existence of the well-posedness for the symmetric vector quasi-equilibrium problem in real locally convex Hausdorff topological vector spaces. The results presented in this paper generalize and extend Theorem 4.2 of [16] and Theorem 4.1 of [20].…”

“…Recently, Han and Gong [19] studied the generalized Levitin-Polyak well-posedness of symmetric strong vector quasiequilibrium problems. Deng and Xiang [20] introduced and studied the generalized well-posedness for the generalized vector equilibrium, which unifies its Hadamard and Levitin-Polyak well-posedness.…”

Well-posedness for a class of strong vector equilibrium problems

“…Various types of well-posedness for (VEP) have been intensively studied in the literature, such as [4,6,18,33]. By using a scalarization method, Li et al [18] introduced two types of Levitin-Polyak well-posedness for (VEP) with variable domination structures and gave sufficient conditions and metric characterizations of Levitin-Polyak well-posedness for (VEP).…”

“…By using a scalarization method, Li et al [18] introduced two types of Levitin-Polyak well-posedness for (VEP) with variable domination structures and gave sufficient conditions and metric characterizations of Levitin-Polyak well-posedness for (VEP). Using the bounded rationality model (see, [2,29,30]), Deng and Xiang [6] introduced and studied wellposedness in connection with generalized vector equilibrium problems, which unifies its Hadamard and Levitin-Polyak well-posedness. Zhang et al [33] extended the result of [6] to symmetric vector qusiequilibrium problems.…”

“…Using the bounded rationality model (see, [2,29,30]), Deng and Xiang [6] introduced and studied wellposedness in connection with generalized vector equilibrium problems, which unifies its Hadamard and Levitin-Polyak well-posedness. Zhang et al [33] extended the result of [6] to symmetric vector qusiequilibrium problems.…”