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A general class of relative optimization problems

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  • I. V. Konnov

    (Kazan Federal University)

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.

Suggested Citation

  • I. V. Konnov, 2021. "A general class of relative optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 501-520, June.
    • Handle: RePEc:spr:mathme:v:93:y:2021:i:3:d:10.1007_s00186-021-00741-1
    DOI: 10.1007/s00186-021-00741-1
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    References listed on IDEAS

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    1. I. V. Konnov, 2019. "Equilibrium formulations of relative optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(1), pages 137-152, August.
    2. Harker, Patrick T., 1991. "Generalized Nash games and quasi-variational inequalities," European Journal of Operational Research, Elsevier, vol. 54(1), pages 81-94, September.
    3. Alexander J. Zaslavski, 2006. "Existence and Structure of Solutions of Autonomous Discrete Time Optimal Control Problems," Lecture Notes in Economics and Mathematical Systems, in: Alberto Seeger (ed.), Recent Advances in Optimization, pages 251-268, Springer.
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