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Multiplicative perturbation analysis for QR factorizations
Stability analysis of parametric variational systems
1. | College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China, China |
References:
[1] |
F. J. Aragón Artacho and B. S. Mordukhovich, Metric regularity and Lipschitzian stability of parametric variational systems,, Nonlinear Analysis, 72 (2010), 1149.
doi: doi:10.1016/j.na.2009.07.051. |
[2] |
F. J. Aragón Artacho and B. S. Mordukhovich, Enhanced metric regularity and Lipschitzian properties of variational systems,, Journal of Global Optimization, 50 (2011), 145.
doi: doi:10.1007/s10898-011-9698-x. |
[3] |
J. P. Aubin and I. Ekeland, "Applied Nonlinear Analysis,", John Wiley and Sons, (1984).
|
[4] |
E. Bednarczuk, Upper Hölder continuity of minimal points,, Journal on Convex Analysis, 9 (2002), 327.
|
[5] |
E. Bednarczuk, Weak sharp efficiency and growth condition for vector-valued functions with applications,, Optimization, 53 (2004), 455.
doi: doi:10.1080/02331930412331330478. |
[6] |
J. M. Borwein, Stability and regular points of inequality systems,, Journal of Optimization Theory and Applications, 48 (1986), 9.
|
[7] |
J. M. Borwein and Q. J. Zhu, "Techniques of Variational Analysis,", Springer, (2005).
|
[8] |
N. H. Chieu, J. C. Yao and N. D. Yen, Relationships between Robinson metric regularity and Lipschitz-like behavior of implicit multifunctions,, Nonlinear Analysis, 72 (2010), 3594.
doi: doi:10.1016/j.na.2009.12.039. |
[9] |
P. H. Dien and N. D. Yen, On implicit function theorems for set-valued maps and their application to mathematical programming under inclusion constraints,, Applied Mathematics and Optimization, 24 (1991), 35.
doi: doi:10.1007/BF01447734. |
[10] |
A. L. Dontchev, M. Quincampoix and N. Zlateva, Aubin criterion for metric regularity,, Journal of Convex Analysis, 13 (2006), 281.
|
[11] |
I. Ekeland, On the variational principle,, Journal of Mathematical Analysis and Applications, 47 (1974), 324.
doi: doi:10.1016/0022-247X(74)90025-0. |
[12] |
N. Q. Huy and J. C. Yao, Stability of implicit multifunctions in Asplund spaces,, Taiwanese Journal of Mathematics, 13 (2009), 47.
|
[13] |
V. Jeyakumar and N. D. Yen, Solution stability of nonsmooth continuous systems with applications to cone-constrained optimization,, SIAM Journal on Optimization, 14 (2004), 1106.
doi: doi:10.1137/S1052623402419236. |
[14] |
B. T. Kien, On the lower semicontinuity of optimal solution sets,, Optimization, 54 (2005), 123.
doi: doi:10.1080/02331930412331330379. |
[15] |
Y. S. Ledyaev and Q. J. Zhu, Implicit multifunctions theorems,, Set-Valued Analysis, 7 (1999), 209.
doi: doi:10.1023/A:1008775413250. |
[16] |
G. M. Lee, N. N. Tam and N. D. Yen, Normal coderivative for multifunctions and implicit function theorems,, Journal of Mathematical Analysis and Applications, 338 (2008), 11.
doi: doi:10.1016/j.jmaa.2007.05.001. |
[17] |
M. H. Li and S. J. Li, Robinson metric regularity of parametric variational systems,, Nonlinear Analysis, 74 (2011), 2262.
doi: doi:10.1016/j.na.2010.11.031. |
[18] |
B. S. Mordukhovich, "Variational Analysis and Generalized Differentiation, Vol. I: Basic Theory, Vol. II: Applications,", Springer, (2006).
|
[19] |
H. V. Ngai and M. Théra, Error bounds and implicit multifunction theorem in smooth Banach spaces and applications to optimization,, Set-Valued Analysis, 12 (2004), 195.
doi: doi:10.1023/B:SVAN.0000023396.58424.98. |
[20] |
S. M. Robinson, Stability theory for systems of inequalities, I. Linear systems,, SIAM Journal on Numerical Analysis, 12 (1975), 754.
doi: doi:10.1137/0712056. |
[21] |
S. M. Robinson, Stability theory for systems of inequalities, II. Differentiable nonlinear systems,, SIAM Journal on Numerical Analysis, 13 (1976), 497.
doi: doi:10.1137/0713043. |
[22] |
S. M. Robinson, Generalized equations and their solutions, Part I, Basic theory,, Mathematical Programming Study, 10 (1979), 128.
|
[23] |
S. M. Robinson, Regularity and stability for convex multivalued functions,, Mathematics of Operations Research, 1 (1976), 130.
doi: doi:10.1287/moor.1.2.130. |
[24] |
A. Uderzo, On some regularity properties in variational analysis,, Set-Valued and Variational Analysis, 17 (2009), 409.
doi: doi:10.1007/s11228-009-0121-4. |
[25] |
N. D. Yen and J. C. Yao, Point-based sufficient conditions for metric regularity of implicit multifunctions,, Nonlinear Analysis, 70 (2009), 2806.
doi: doi:10.1016/j.na.2008.04.005. |
[26] |
N. D. Yen, J. C. Yao and B. T. Kien, Covering properties at positive-order rates of multifunctions and some related topics,, Journal of Mathematical Analysis and Applications, 338 (2008), 467.
doi: doi:10.1016/j.jmaa.2007.05.041. |
show all references
References:
[1] |
F. J. Aragón Artacho and B. S. Mordukhovich, Metric regularity and Lipschitzian stability of parametric variational systems,, Nonlinear Analysis, 72 (2010), 1149.
doi: doi:10.1016/j.na.2009.07.051. |
[2] |
F. J. Aragón Artacho and B. S. Mordukhovich, Enhanced metric regularity and Lipschitzian properties of variational systems,, Journal of Global Optimization, 50 (2011), 145.
doi: doi:10.1007/s10898-011-9698-x. |
[3] |
J. P. Aubin and I. Ekeland, "Applied Nonlinear Analysis,", John Wiley and Sons, (1984).
|
[4] |
E. Bednarczuk, Upper Hölder continuity of minimal points,, Journal on Convex Analysis, 9 (2002), 327.
|
[5] |
E. Bednarczuk, Weak sharp efficiency and growth condition for vector-valued functions with applications,, Optimization, 53 (2004), 455.
doi: doi:10.1080/02331930412331330478. |
[6] |
J. M. Borwein, Stability and regular points of inequality systems,, Journal of Optimization Theory and Applications, 48 (1986), 9.
|
[7] |
J. M. Borwein and Q. J. Zhu, "Techniques of Variational Analysis,", Springer, (2005).
|
[8] |
N. H. Chieu, J. C. Yao and N. D. Yen, Relationships between Robinson metric regularity and Lipschitz-like behavior of implicit multifunctions,, Nonlinear Analysis, 72 (2010), 3594.
doi: doi:10.1016/j.na.2009.12.039. |
[9] |
P. H. Dien and N. D. Yen, On implicit function theorems for set-valued maps and their application to mathematical programming under inclusion constraints,, Applied Mathematics and Optimization, 24 (1991), 35.
doi: doi:10.1007/BF01447734. |
[10] |
A. L. Dontchev, M. Quincampoix and N. Zlateva, Aubin criterion for metric regularity,, Journal of Convex Analysis, 13 (2006), 281.
|
[11] |
I. Ekeland, On the variational principle,, Journal of Mathematical Analysis and Applications, 47 (1974), 324.
doi: doi:10.1016/0022-247X(74)90025-0. |
[12] |
N. Q. Huy and J. C. Yao, Stability of implicit multifunctions in Asplund spaces,, Taiwanese Journal of Mathematics, 13 (2009), 47.
|
[13] |
V. Jeyakumar and N. D. Yen, Solution stability of nonsmooth continuous systems with applications to cone-constrained optimization,, SIAM Journal on Optimization, 14 (2004), 1106.
doi: doi:10.1137/S1052623402419236. |
[14] |
B. T. Kien, On the lower semicontinuity of optimal solution sets,, Optimization, 54 (2005), 123.
doi: doi:10.1080/02331930412331330379. |
[15] |
Y. S. Ledyaev and Q. J. Zhu, Implicit multifunctions theorems,, Set-Valued Analysis, 7 (1999), 209.
doi: doi:10.1023/A:1008775413250. |
[16] |
G. M. Lee, N. N. Tam and N. D. Yen, Normal coderivative for multifunctions and implicit function theorems,, Journal of Mathematical Analysis and Applications, 338 (2008), 11.
doi: doi:10.1016/j.jmaa.2007.05.001. |
[17] |
M. H. Li and S. J. Li, Robinson metric regularity of parametric variational systems,, Nonlinear Analysis, 74 (2011), 2262.
doi: doi:10.1016/j.na.2010.11.031. |
[18] |
B. S. Mordukhovich, "Variational Analysis and Generalized Differentiation, Vol. I: Basic Theory, Vol. II: Applications,", Springer, (2006).
|
[19] |
H. V. Ngai and M. Théra, Error bounds and implicit multifunction theorem in smooth Banach spaces and applications to optimization,, Set-Valued Analysis, 12 (2004), 195.
doi: doi:10.1023/B:SVAN.0000023396.58424.98. |
[20] |
S. M. Robinson, Stability theory for systems of inequalities, I. Linear systems,, SIAM Journal on Numerical Analysis, 12 (1975), 754.
doi: doi:10.1137/0712056. |
[21] |
S. M. Robinson, Stability theory for systems of inequalities, II. Differentiable nonlinear systems,, SIAM Journal on Numerical Analysis, 13 (1976), 497.
doi: doi:10.1137/0713043. |
[22] |
S. M. Robinson, Generalized equations and their solutions, Part I, Basic theory,, Mathematical Programming Study, 10 (1979), 128.
|
[23] |
S. M. Robinson, Regularity and stability for convex multivalued functions,, Mathematics of Operations Research, 1 (1976), 130.
doi: doi:10.1287/moor.1.2.130. |
[24] |
A. Uderzo, On some regularity properties in variational analysis,, Set-Valued and Variational Analysis, 17 (2009), 409.
doi: doi:10.1007/s11228-009-0121-4. |
[25] |
N. D. Yen and J. C. Yao, Point-based sufficient conditions for metric regularity of implicit multifunctions,, Nonlinear Analysis, 70 (2009), 2806.
doi: doi:10.1016/j.na.2008.04.005. |
[26] |
N. D. Yen, J. C. Yao and B. T. Kien, Covering properties at positive-order rates of multifunctions and some related topics,, Journal of Mathematical Analysis and Applications, 338 (2008), 467.
doi: doi:10.1016/j.jmaa.2007.05.041. |
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