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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 71, 2022 - Issue 3
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Articles

Semicontinuity of the solution maps to vector equilibrium problems with equilibrium constraints

Pages 737-751 | Received 04 Jun 2020, Accepted 07 Aug 2020, Published online: 26 Aug 2020

References

  • Muu LD, Oettli W. Convergence of an adaptive penalty scheme for finding constrained equilibria. Nonlinear Anal. 1992;18(12):1159–1166.
  • Suantai S, Petrot N. Existence and stability of iterative algorithms for the system of nonlinear quasi-mixed equilibrium problems. Appl Math Lett. 2011;24(3):308–313.
  • Ansari QH. Existence of solutions of systems of generalized implicit vector quasi-equilibrium problems. J Math Anal Appl. 2008;341(2):1271–1283.
  • Bianchi M, Hadjisavvas N, Schaible S. Vector equilibrium problems with generalized monotone bifunctions. J Optim Theory Appl. 1997;92(3):527–542.
  • Hai NX, Khanh PQ. Existence of solutions to general quasiequilibrium problems and applications. J Optim Theory Appl. 2007;133(3):317–327.
  • Sadeghi S, Mirdehghan SM. Stability of local efficiency in multiobjective optimization. J Optim Theory Appl. 2018;178(2):591–613.
  • Kapoor S, Lalitha CS. Stability and scalarization for a unified vector optimization problem. J Optim Theory Appl. 2019;182(3):1050–1067.
  • Huyen DTK, Yao JC, Yen ND. Sensitivity analysis of a stationary point set map under total perturbations. Part 1: Lipschitzian stability. J Optim Theory Appl. 2019;180(1):91–116.
  • Huyen DTK, Yao JC, Yen ND. Sensitivity analysis of a stationary point set map under total perturbations. Part 2: Robinson stability. J Optim Theory Appl. 2019;180(1):117–139.
  • Anh LQ, Khanh PQ. Semicontinuity of the solution set of parametric multivalued vector quasiequilibrium problems. J Math Anal Appl. 2004;294(2):699–711.
  • Anh LQ, Khanh PQ. Various kinds of semicontinuity and the solution sets of parametric multivalued symmetric vector quasiequilibrium problems. J Global Optim. 2008;41(4):539–558.
  • Anh LQ, Khanh PQ. Continuity of solution maps of parametric quasiequilibrium problems. J Global Optim. 2010;46(2):247–259.
  • Chen CR, Li SJ, Teo KL. Solution semicontinuity of parametric generalized vector equilibrium problems. J Global Optim. 2009;45(2):309–318.
  • Kim WK, Kum S, Lee KH. Semicontinuity of the solution multifunctions of the parametric generalized operator equilibrium problems. Nonlinear Anal Theory, Methods Appl. 2009;71(12):2182–2187.
  • Li X, Li S. Continuity of approximate solution mappings for parametric equilibrium problems. J Global Optim. 2011;51(3):541–548.
  • Xu S, Li SJ. A new proof approach to lower semicontinuity for parametric vector equilibrium problems. Optim Lett. 2009;3(3):453–459.
  • Xu Y, Li S. On the lower semicontinuity of the solution mappings to a parametric generalized strong vector equilibrium problem. Positivity. 2013;17(2):341–353.
  • Anh LQ, Khanh PQ. Uniqueness and Hölder continuity of the solution to multivalued equilibrium problems in metric spaces. J Global Optim. 2007;37(3):449–465.
  • Anh LQ, Khanh PQ. On the Hölder continuity of solutions to parametric multivalued vector equilibrium problems. J Math Anal Appl. 2006;321(1):308–315.
  • Anh LQ, Khanh PQ. Sensitivity analysis for multivalued quasiequilibrium problems in metric spaces: Hölder continuity of solutions. J Global Optim. 2008;42(4):515–531.
  • Anh LQ, Duoc PT, Tam TN. On Hölder continuity of solution maps to parametric vector primal and dual equilibrium problems. Optim. 2018;67(8):1169–1182.
  • Li S, Chen C, Li X, et al. Hölder continuity and upper estimates of solutions to vector quasiequilibrium problems. Eur J Oper Res. 2011;210(2):148–157.
  • Li S, Li X, Wang L, et al. The hölder continuity of solutions to generalized vector equilibrium problems. Eur J Oper Res. 2009;199(2):334–338.
  • Outrata JV. Optimality conditions for a class of mathematical programs with equilibrium constraints. Math Oper Res. 1999;24(3):627–644.
  • Outrata JV. A generalized mathematical program with equilibrium constraints. SIAM J Control Optim. 2000;38(5):1623–1638.
  • Bao TQ, Mordukhovich P, Gupta BS. Necessary conditions in multiobjective optimization with equilibrium constraints. J Optim Theory Appl. 2007;135(2):179–203.
  • Mordukhovich BS. Characterizations of linear suboptimality for mathematical programs with equilibrium constraints. Math Program. 2009;120(1):261–283.
  • Lignola MB, Morgan J. Well-posedness for optimization problems with constraints defined by variational inequalities having a unique solution. J Global Optim. 2000;16(1):57–67.
  • Lignola MB, Morgan J. α-well-posedness for Nash equilibria and for optimization problems with Nash equilibrium constraints. J Global Optim. 2006;36(3):439–459.
  • Anh LQ, Hung N. Levitin–Polyak well-posedness for strong bilevel vector equilibrium problems and applications to traffic network problems with equilibrium constraints. Positivity. 2018;22(5):1223–1239.
  • Anh LQ, Khanh PQ, Van DTM. Well-posedness under relaxed semicontinuity for bilevel equilibrium and optimization problems with equilibrium constraints. J Optim Theory Appl. 2012;153(1):42–59.
  • Mordukhovich BS. Variational analysis and applications. Berlin: Springer; 2018.
  • Aubin JP, Frankowska H. Set-valued analysis. Boston (MA): Birhäuser; 1990.
  • Hu S, Papageorgiou N. Handbook of multivalued analysis, volume I: theory. Boston (MA): Kluwer; 1997.
  • Kuroiwa D. Convexity for set-valued maps. Appl Math Lett. 1996;9(2):97–101.
  • Tanaka T. Generalized quasiconvexities, cone saddle points, and minimax theorem for vector-valued functions. J Optim Theory Appl. 1994;81(2):355–377.
  • Göpfert A, Riahi H, Tammer C, et al. Variational methods in partially ordered spaces. New York (NY): Springer Science & Business Media; 2006.

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