Approximate duality for vector quasi-equilibrium problems and applications. (English) Zbl 1213.90246
Summary: We introduce new versions of \(\varepsilon\)-dual problems of a vector quasi-equilibrium problem with set-valued maps, and we give an \(\varepsilon\)-duality result between approximate solutions of the primal and dual problems. As the first application of the main result, we obtain an \(\varepsilon\)-duality for a vector quasi-equilibrium problem whose \(\varepsilon\)-solutions are understood in the sense of proper efficiency. The second application is devoted to an \(\varepsilon\)-duality for a vector optimization problem with set-valued maps.
MSC:
| 90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |
| 90C46 | Optimality conditions and duality in mathematical programming |
| 90C29 | Multi-objective and goal programming |
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