Abstract
We consider relative or subjective optimization problems where the goal function and feasible set are dependent on the current state of the system under consideration. In general, they are formulated as quasi-equilibrium problems, hence finding their solutions may be rather difficult. We describe a rather general class of relative optimization problems in metric spaces, which in addition depend on the starting state. We also utilize quasi-equilibrium type formulations of these problems and show that they admit rather simple descent solution methods. This approach gives suitable trajectories tending to a relatively optimal state. We describe several examples of applications of these problems. Preliminary results of computational experiments confirmed efficiency of the proposed method.
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Acknowledgements
In this work, the author was supported by Russian Foundation for Basic Research, Project No. 19-01-00431. The author is grateful to referees for their valuable comments.
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Konnov, I.V. A general class of relative optimization problems. Math Meth Oper Res 93, 501–520 (2021). https://doi.org/10.1007/s00186-021-00741-1
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DOI: https://doi.org/10.1007/s00186-021-00741-1