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Optimal Control of Problems Governed by Mixed Quasi-Equilibrium Problems Under Monotonicity-Type Conditions with Applications

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Abstract

The main goal of this paper is to study the existence of solutions for optimal control problems governed by mixed quasi-equilibrium problems under monotonicity type conditions. More precisely, the state control system takes the general form of a mixed quasi-equilibrium problem described by the sum of a maximal monotone bifunction and a pseudomonotone bifunction in the sense of Brézis. As applications, we study the existence of solutions for optimal control problems governed by quasi-variational inequalities. In particularly, we consider the optimal control of an evolutionary quasi-variational inequality described by a p-Laplacian type operator. The results obtained in this paper are new and can be applied to the study of optimal control of a variety of systems whose formulations can be presented as a mixed equilibrium problem.

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Acknowledgements

This research was supported by KFUPM funded Research Project # IN161003 and it was done during the visit of first two authors. Authors are grateful to KFUPM for proving excellent research facilities to carry out this work. Authors are grateful to the referees and handling editor for their valuable suggestions and comments which improved the previous version of this paper.

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Authors and Affiliations

  1. Department of Economics, Faculty of Economics and Social Sciences, Ibn Zohr University, B.P. 8658, Poste Dakhla, Agadir, Morocco

    O. Chadli

  2. Department of Mathematics, Aligarh Muslim University, Aligarh, 202 002, India

    Q. H. Ansari

  3. Department of Mathematics & Statistics, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia

    Q. H. Ansari, S. Al-Homidan & M. Alshahrani

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  1. O. Chadli
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  2. Q. H. Ansari
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  3. S. Al-Homidan
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  4. M. Alshahrani
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Correspondence to Q. H. Ansari.

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Chadli, O., Ansari, Q.H., Al-Homidan, S. et al. Optimal Control of Problems Governed by Mixed Quasi-Equilibrium Problems Under Monotonicity-Type Conditions with Applications. Appl Math Optim 83, 2185–2209 (2021). https://doi.org/10.1007/s00245-019-09623-9

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