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On Well-Posedness of Some Constrained Variational Problems

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  • Savin Treanţă

    (Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania)

Abstract

By considering the new forms of the notions of lower semicontinuity, pseudomonotonicity, hemicontinuity and monotonicity of the considered scalar multiple integral functional, in this paper we study the well-posedness of a new class of variational problems with variational inequality constraints. More specifically, by defining the set of approximating solutions for the class of variational problems under study, we establish several results on well-posedness.

Suggested Citation

  • Savin Treanţă, 2021. "On Well-Posedness of Some Constrained Variational Problems," Mathematics, MDPI, vol. 9(19), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2478-:d:649671
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    References listed on IDEAS

    as
    1. L. C. Ceng & N. Hadjisavvas & S. Schaible & J. C. Yao, 2008. "Well-Posedness for Mixed Quasivariational-Like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 109-125, October.
    2. Ya-Ping Fang & Rong Hu, 2007. "Estimates of approximate solutions and well-posedness for variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(2), pages 281-291, April.
    3. M. B. Lignola, 2006. "Well-Posedness and L-Well-Posedness for Quasivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 128(1), pages 119-138, January.
    4. Jia-Wei Chen & Zhongping Wan & Yeol Cho, 2013. "Levitin–Polyak well-posedness by perturbations for systems of set-valued vector quasi-equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(1), pages 33-64, February.
    5. Yi-bin Xiao & Xinmin Yang & Nan-jing Huang, 2015. "Some equivalence results for well-posedness of hemivariational inequalities," Journal of Global Optimization, Springer, vol. 61(4), pages 789-802, April.
    6. X. X. Huang, 2001. "Extended and strongly extended well-posedness of set-valued optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 53(1), pages 101-116, April.
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