On the characterization of the solution set for vector equilibrium problem. (English) Zbl 1412.90136
Summary: In this article, we investigate the nonemptiness and compactness of the solution set for vector equilibrium problem defined in finite-dimensional spaces. We show that vector equilibrium problem has nonempty and compact solution set if and only if linearly scalarized equilibrium problem has nonempty and compact solution set provided that \(R_1=\{0\}\) holds. Furthermore, we obtain that vector equilibrium problem has nonempty and compact solution set if and only if linearly scalarized equilibrium problem has nonempty and compact solution set when coercivity condition holds. As applications, we employ the obtained results to derive Levitin-Polyak well-posedness, stability analysis and connectedness of the solution set of the vector equilibrium problem.
MSC:
| 90C29 | Multi-objective and goal programming |
| 90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |
Keywords:
vector equilibrium problem; nonemptiness and compactness; asymptotic cone; coercivity conditionReferences:
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