Abstract
We consider relative or subjective optimization problems where the goal function and feasible set are dependent of the current state of the system under consideration. We propose equilibrium formulations of the corresponding problems that lead to general (quasi-)equilibrium problems. We propose to apply a regularized version of the penalty method for the general quasi-equilibrium problem, which enables us to establish existence results under weak coercivity conditions and replace the quasi-equilibrium problem with a sequence of the usual equilibrium problems. We describe several examples of applications and show that the subjective approach can be extended to non-cooperative game problems.
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Acknowledgements
The results of this work were obtained within the state assignment of the Ministry of Science and Education of Russia, Project No. 1.460.2016/1.4. In this work, the author was also supported by Russian Foundation for Basic Research, Project No. 16-01-00109a.
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Konnov, I.V. Equilibrium formulations of relative optimization problems. Math Meth Oper Res 90, 137–152 (2019). https://doi.org/10.1007/s00186-019-00663-z
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DOI: https://doi.org/10.1007/s00186-019-00663-z
Keywords
- Relative optimization
- Quasi-equilibrium problems
- Equilibrium problems
- Regularized penalty method
- Existence results
- Coercivity conditions
- Non-cooperative games