Abstract
In this paper, we consider well-posedness of symmetric vector quasi-equilibrium problems. Based on a nonlinear scalarization technique, we first establish the bounded rationality model M for symmetric vector quasi-equilibrium problems, and then introduce a well-posedness concept for symmetric vector quasi-equilibrium problems, which unifies its Hadamard and Tykhonov well-posedness. Finally, sufficient conditions on the well-posedness for symmetric vector quasi-equilibrium problems are given.
Highlights
1 Introduction In, Fu [ ] introduced the symmetric vector quasi-equilibrium problem which is a generalization of equilibrium problem proposed by Blum and Oettli [ ] and gave an existence theorem for a weak Pareto solution for (SVQEP)
In, Farajzadeh [ ] considered existence theorem of the solution of (SVQEP) in the Hausdorff topological vector space
The notion of extended well-posedness for vector optimization problems has been investigated in [ ]. In some sense this notion unifies the ideas of Tykhonov and Hadamard well-posedness, allowing perturbations of the objective function and the feasible set
Summary
In , Fu [ ] introduced the symmetric vector quasi-equilibrium problem (for short, SVQEP) which is a generalization of equilibrium problem proposed by Blum and Oettli [ ] and gave an existence theorem for a weak Pareto solution for (SVQEP). The notion of extended well-posedness for vector optimization problems has been investigated in [ ] In some sense this notion unifies the ideas of Tykhonov and Hadamard well-posedness, allowing perturbations of the objective function and the feasible set. Wellposedness under perturbations (called parametric well-posedness) for vector equilibrium problems has been investigated in [ ] This kind of well-posedness is a blending of Hadamard and Tikhonov notions, and it gives links to stability theory and seems well adapted to describe the behaviors of solutions under perturbations.
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