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.
Highlights
As is well known, the notion of well-posedness can be divided into two different groups: Hadamard type and Tykhonov type [ ]
Tykhonov types of well-posedness for a problem such as Tykhonov and Levitin-Polyak well-posedness are based on the convergence of approximating solution sequences of the problem
The notion of extended well-posedness has been generalized to vector optimization problems by Huang [ – ]
Summary
The notion of well-posedness can be divided into two different groups: Hadamard type and Tykhonov type [ ]. We observe that the scalarization technique is an efficient approach to deal with Tykhonov types well-posedness for vector optimization problems. Miglierina et al [ ] investigated several types of well-posedness concepts for vectorial optimization problems by using a nonlinear scalarization procedure.
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