References
Cánovas MJ, López MA, Parra J (2005) Stability of linear inequality systems in a parametric setting. J Optim Theory Appl 125:275–297
Cánovas MJ, Dontchev AL, López MA, Parra J (2009) Isolated calmness of solution mappings in convex semi-infinite optimization. J Math Anal Appl 350:829–837
Gaya VE, López MA, Vera de Serio VN (2003) Stability in convex semi-infinite programming and rates of convergence of optimal solutions of discretized finite subproblems. Optimization 52:693–713
Goberna MA, Jeyakumar V, Li G, López MA (2011) Robust linear semi-infinite programming duality under uncertainty. Submitted
Hu H (2000) Perturbation analysis of global error bounds for systems of linear inequalities. Math Program, Ser B 88:277–284. Error bounds in mathematical programming (Kowloon, 1998)
Hu H (2003) On uniform global error bounds for convex inequalities. J Glob Optim 25:237–242
Hu H (2007) Characterizations of local and global error bounds for convex inequalities in Banach spaces. SIAM J Optim 18:309–321
Kruger A, Ngai HV, Théra M (2010) Stability of error bounds for convex constraint systems in Banach spaces. SIAM J Optim 20:3280–3296
López MA, Vera de Serio VN (2001) Stability of the feasible set mapping in convex semi-infinite programming. In: Semi-infinite programming, Alicante, 1999. Nonconvex Optim Appl, vol 57. Kluwer Academic, Dordrecht, pp 101–120
López MA, Vera de Serio VN (2007) Stability of inequality systems involving max-type functions. Pac J Optim 3:361–378
López MA, Rubinov AM, Vera de Serio VN (2005a) Stability of the lower level sets of ICAR functions. Numer Funct Anal Optim 26:113–127
López MA, Rubinov AM, Vera de Serio VN (2005b) Stability of semi-infinite inequality systems involving min-type functions. Numer Funct Anal Optim 26:81–112
López MA, Ridolfi A, Vera de Serio VN (2011) On coderivatives and Lipschitzian properties of the dual pair in optimization. Nonlinear Anal. doi:10.1016/j.na.2011.06.036
Lucchetti R (2000) Convexity and well-posed problems. Springer, Berlin
Ngai HV, Kruger A, Théra M (2010) Stability of error bounds for semi-infinite convex constraint systems. SIAM J Optim 20:2080–2096
Shapiro A (2001) Rates of convergence of optimal solutions of discretized semi-infinite programming problems. Working Paper, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta (Georgia)
Still G (2001) Discretization in semi-infinite programming: the rate of convergence. Math Program 91:53–69
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This rejoinder refers to the comments available at doi:10.1007/s11750-011-0214-8, doi:10.1007/s11750-011-0215-7, doi:10.1007/s11750-011-0216-6, doi:10.1007/s11750-011-0217-5, doi:10.1007/s11750-011-0218-4, doi:10.1007/s11750-011-0219-3, doi:10.1007/s11750-011-0220-x.
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López, M.A. Rejoinder on: Stability in linear optimization and related topics. A personal tour. TOP 20, 270–278 (2012). https://doi.org/10.1007/s11750-011-0225-5
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DOI: https://doi.org/10.1007/s11750-011-0225-5