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A new class of generalized \(f\)-projected dynamical system in Banach spaces. (English) Zbl 1311.37079
Summary: In this article, a new class of generalized \(f\)-projected dynamical systems is introduced and studied in Banach spaces. A global existence and uniqueness result of generalized \(f\)-projected dynamical system is proved, which generalizes the existence result of Y. S. Xia and J. Wang [J. Optimization Theory Appl. 106, No. 1, 129–150 (2000; Zbl 0971.37013)]. The global convergence stability of the generalized \(f\)-projected dynamical system and the sensitivity result of solutions set with perturbations of the constraint sets are also obtained under some suitable conditions.
MSC:
37N40 Dynamical systems in optimization and economics
37C75 Stability theory for smooth dynamical systems
90C31 Sensitivity, stability, parametric optimization
49J40 Variational inequalities
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[1] DOI: 10.1007/BF02073589 · Zbl 0785.93044 · doi:10.1007/BF02073589
[2] DOI: 10.1287/opre.42.6.1120 · Zbl 0823.90037 · doi:10.1287/opre.42.6.1120
[3] DOI: 10.1016/S0893-9659(04)90026-2 · Zbl 1058.49008 · doi:10.1016/S0893-9659(04)90026-2
[4] DOI: 10.1017/S0004972700038892 · Zbl 1104.47053 · doi:10.1017/S0004972700038892
[5] DOI: 10.1016/j.camwa.2007.01.029 · Zbl 1151.47057 · doi:10.1016/j.camwa.2007.01.029
[6] DOI: 10.1016/0362-546X(91)90200-K · Zbl 0757.46033 · doi:10.1016/0362-546X(91)90200-K
[7] DOI: 10.1007/BF02192301 · Zbl 0837.93063 · doi:10.1007/BF02192301
[8] DOI: 10.1023/A:1004611224835 · Zbl 0971.37013 · doi:10.1023/A:1004611224835
[9] Zou YZ, Impul. Dyn. Sys. Appl. 4 pp 233– (2006)
[10] Alber Y, Funct. Differ. Eqns. 1 pp 1– (1994)
[11] DOI: 10.1016/j.jmaa.2004.11.007 · Zbl 1129.47043 · doi:10.1016/j.jmaa.2004.11.007
[12] DOI: 10.1016/j.na.2009.01.082 · Zbl 1217.47108 · doi:10.1016/j.na.2009.01.082
[13] DOI: 10.1023/B:JOTA.0000042598.21226.af · Zbl 1082.34043 · doi:10.1023/B:JOTA.0000042598.21226.af
[14] Alber Y, Theory and Applications of Nonlinear Operators of Accretive and Monotone Type pp 15– (1996)
[15] Alber Y, Analysis 21 pp 17– (2001) · Zbl 0985.47044 · doi:10.1524/anly.2001.21.1.17
[16] DOI: 10.1016/j.na.2008.04.019 · Zbl 1167.49031 · doi:10.1016/j.na.2008.04.019
[17] DOI: 10.1016/j.na.2008.08.008 · Zbl 1219.47110 · doi:10.1016/j.na.2008.08.008
[18] Li X, Acta Math. Sinica, Chin. Ser. 54 pp 811– (2011)
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