Abstract
We use asymptotic analysis for studying noncoercive pseudomonotone equilibrium problems and vector equilibrium problems. We introduce suitable notions of asymptotic functions, which provide sufficient conditions for the set of solutions of these problems to be nonempty and compact under quasiconvexity of the objective function. We characterize the efficient and weakly efficient solution set for the nonconvex vector equilibrium problem via scalarization. A sufficient condition for the closedness of the image of a nonempty, closed and convex set via a quasiconvex vector-valued function is given. Finally, applications to the quadratic fractional programming problem are also presented.
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Acknowledgements
The authors want to express their gratitude to both referees for their criticism and suggestions that helped to improve this paper. The research for the second author was partially supported by Conicyt–Chile under project Fondecyt Postdoctorado 3160205.
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Iusem, A., Lara, F. Optimality Conditions for Vector Equilibrium Problems with Applications. J Optim Theory Appl 180, 187–206 (2019). https://doi.org/10.1007/s10957-018-1321-6
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DOI: https://doi.org/10.1007/s10957-018-1321-6
Keywords
- Asymptotic analysis
- Generalized convexity
- Pseudomonotone operators
- Equilibrium problems
- Vector optimization