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Topological Methods in Nonlinear Analysis

Levitin-Polyak Well-posedness by perturbations for bilevel mixed vector variational inequalities
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  • Levitin-Polyak Well-posedness by perturbations for bilevel mixed vector variational inequalities
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Levitin-Polyak Well-posedness by perturbations for bilevel mixed vector variational inequalities

Autor

  • Wenbin Wei
  • Yirong Jiang https://orcid.org/0000-0003-0324-8637
  • Guoji Tang https://orcid.org/0000-0001-9869-9291

DOI:

https://doi.org/10.12775/TMNA.2025.029

Słowa kluczowe

Bilevel mixed vector variational inequalities, Levitin-Polyak well-posedness by perturbations

Abstrakt

The purpose of this paper is to investigate the Levitin-Polyak well-posedness by perturbations of the bilevel mixed vector variational inequality (in short, BMVVI). Under suitable conditions, we prove that the Levitin-Polyak well-posedness by perturbations of the BMVVI is equivalent to existence and uniqueness of its solution and the generalized Levitin-Polyak well-posedness by perturbations of the BMVVI is equivalent to the nonemptiness and boundedness of the solution set.

Bibliografia

Y. Alber, The regularization method for variational inequalities with nonsmooth unbounded operator in Banach space, Appl. Math. Lett. 6 (1993), 63–68.

L.Q. Anh and D.V. Hien, On well-posedness for parametric vector quasi equilibrium problems with moving cones, Appl. Math. 61 (2016), 651–668.

L.Q. Anh, P.Q. Khanh and D.T.M. Van, Well-posedness under relaxed semicontinuity for bilevel equilibrium and optimization problems with equilibrium constraints, J. Optim. Theory Appl. 153 (2012), 42–59.

O. Chadli, Q.H. Ansari and S. Al-Homidan, Existence of solutions and algorithms for bilevel vector equilibrium problems: an auxiliary principle technique, J. Optim. Theory Appl. 172 (2017), 726–758.

J.W. Chen, Z.P. Wan and Y.J. Cho, The existence of solutions and well-posedness for bilevel mixed equilibrium problems in banach spaces, Taiwan. J. Math. 17 (2013), 725-748.

P. Cubiotti and J.C. Yao, On the Cauchy problem for a class of differential inclusions with applications, Appl. Anal. 99 (2020), 2543–2554.

K. Fan, A generalization of Tychonoff ’s fixed piont theorem, Math. Ann. 142 (1961), 305-310.

K. Fan, Some properties of convex sets related to fixed point theorems, Math. Ann. 266 (1984), 519–537.

Y.P. Fang and R. Hu, Parametric well-posedness for variational inequalities defined by bifunctions, Comput. Math. Appl. 53 (2007), 1306–1316.

Y.P. Fang, N.J. Huang and J.C. Yao, Well-posedness by perturbations of mixed variational inequalities in Banach spaces, Eur. J. Oper. Res. 201 (2010), 682–692.

Y.P. Fang and N.J. Huang, J.C. Yao, Well-posedness of mixed variational inequalities, inclusion problems and fixed point problems, J. Global Optim. 41 (2008), 117–133.

W. Han and B.D. Reddy, On the finite element method for mixed variational inequalities arising in elastoplasticity, SIAM J. Numer. Anal. 32 (1995), 1778–1807.

R. Hu and Y.P. Fang, Levitin–Polyak well-posedness by perturbations of inverse variational inequalities, Optim. Lett. 7 (2013), 343–359.

R. Hu and Y.P. Fang, Characterizations of Levitin–Polyak well-posedness by perturbations for the split variational inequality problem, Optimization 65 (2016), 1717–1732.

R. Hu and Y.P. Fang, Levitin–Polyak well-posedness by perturbations for the split inverse variational inequality problem, J. Fixed Point Theory Appl. 4 (2016), 785–800.

N.J. Huang and Y.P. Fang, On vector variational inequalities in reflexive Banach spaces, J. Global Optim. 32 (2005), 495–505.

X.X. Ju, X.L. Zhu and M. Akram, Levitin–Polyak well-posedness for bilevel vector variational inequalities, J. Nonlinear Var. Anal. 3 (2019), 277-293.

I.V. Konnov and E.O. Volotskaya, Mixed variational inequalities and economic equilibrium problems, J. Comput. Appl. Math. 2 (2002), 289–314.

K. Kuratowski, Topology, volumes 1 and 2, Academic Press, New York, 1968.

E.S. Levitin and B.T. Polyak, Convergence of minimizing sequences in conditional extremum problems, Sov. Math. Dokl. 7 (1966), 764–767.

S.J. Li and M.H. Li, Levitin–Polyak well-posedness of vector equilibrium problems, Math. Methods Oper. Res. 69 (2009), 125–140.

M.B. Lignola, Well-posedness and L-well-posedness for quasivariational inequalities, J. Optim. Theory Appl. 128 (2006), 119–138.

M.B. Lignola and J. Morgan, Well-posedness for optimization problems with constraints defined by variational inequalities having a unique solution, J. Global Optim. 16 (2000), 57–67.

R. Lucchetti and F. Patrone, Hadamard and Tykhonov well-posedness of certain class of convex functions, J. Math. Anal. Appl. 88 (1982), 204-215.

R. Lucchetti and J. Revalski (eds.), Recent Developments in Well-Posed Variational Problems, Kluwer Academic Publishers, Dordrecht, Holland, 1995.

M. Margiocco, F. Patrone and L. Pusillo, A new approach to Tikhonov well-posedness for Nash equilibria, Optimization 40 (1997), 385–400.

M. Margiocco, F. Patrone and L. Pusillo, Metric characterizations of Tikhonov wellposedness in value, J. Optim. Theory Appl. 100 (1999), 377–387.

M. Margiocco, F. Patrone and L. Pusillo, On the Tikhonov well-posedness of concave games and Cournot oligopoly games, J. Optim. Theory Appl. 112 (2002), 361–379.

J. Morgan, Approximations and well-posedness in multicriteria games, Ann. Oper. Res. 137 (2005), 257–68.

D.R. Sahu, J.C. Yao, M. Verma and K.K. Shukla, Convergence rate analysis of proximal gradient methods with applications to composite minimization problems, Optimization 70 (2021), 75–100.

A.N. Tykhonov, On the stability of the functional optimization problem, USSR J. Comput. Math. Math. Phys. 6 (1966), 631–634.

T. Zolezzi, Well-posedness criteria in optimization with application to the calculus of variations, Nonlinear Anal. 25 (1995), 437–453.

T. Zolezzi, Extended well-posedness of optimization problems, J. Optim. Theory Appl. 91 (1996), 257–266.

Topological Methods in Nonlinear Analysis

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Opublikowane

2025-12-11

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WEI, Wenbin, JIANG, Yirong & TANG, Guoji. Levitin-Polyak Well-posedness by perturbations for bilevel mixed vector variational inequalities. Topological Methods in Nonlinear Analysis [online]. 11 grudzień 2025, s. 1–18. [udostępniono 14.12.2025]. DOI 10.12775/TMNA.2025.029.
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