Characterizations of Stability of Error Bounds for Convex Inequality Constraint Systems (original) (raw)

[1] Malek Abbasi; Michel Théra Strongly regular points of mappings, Fixed Point Theory Algorithms Sci. Eng., Volume 2021 (2021), 14 | MR | Zbl | DOI

[2] A. A. Auslender; Jean-Pierre Crouzeix Global regularity theorems, Math. Oper. Res., Volume 13 (1988) no. 2, pp. 243-253 | MR | DOI | Zbl

[3] Dominique Azé A survey on error bounds for lower semicontinuous functions, ESAIM, Proc., Volume 13 (2003), pp. 1-17 (Proceedings of 2003 MODE-SMAI Conference) | Zbl | MR

[4] Dominique Azé A unified theory for metric regularity of multifunctions, J. Convex Anal., Volume 13 (2006) no. 2, pp. 225-252 | Zbl | MR

[5] Dominique Azé; Jean-Noël Corvellec On the sensitivity analysis of Hoffman constants for systems of linear inequalities, SIAM J. Optim., Volume 12 (2002) no. 4, pp. 913-927 | MR

[6] Dominique Azé; Jean-Noël Corvellec Characterizations of error bounds for lower semicontinuous functions on metric spaces, ESAIM, Control Optim. Calc. Var., Volume 10 (2004), pp. 409-425 | Zbl | Numdam | MR

[7] Heinz H. Bauschke; Jonathan M. Borwein On projection algorithms for solving convex feasibility problems, SIAM Rev., Volume 38 (1996) no. 3, pp. 367-426 | Zbl | MR | DOI

[8] Amir Beck; Marc Teboulle Convergence rate analysis and error bounds for projection algorithms in convex feasibility problems, Optim. Methods Softw., Volume 18 (2003) no. 4, pp. 377-394 | Zbl | MR | DOI

[9] Ewa M. Bednarczuk; Alexander Y. Kruger Error bounds for vector-valued functions: necessary and sufficient conditions, Nonlinear Anal., Theory Methods Appl., Volume 75 (2012) no. 3, pp. 1124-1140 | DOI | Zbl | MR

[10] James V. Burke; Sien Deng Weak sharp minima revisited. I. Basic theory, Control Cybern., Volume 31 (2002) no. 3, pp. 439-469 | Zbl | MR

[11] James V. Burke; Sien Deng Weak sharp minima revisited. II. Application to linear regularity and error bounds, Math. Program., Volume 104 (2005) no. 2-3, pp. 235-261 | Zbl | MR | DOI

[12] María J. Cánovas; Alexander Y. Kruger; Marco A. López; Juan Parra; Michel Théra Calmness modulus of linear semi-infinite programs, SIAM J. Optim., Volume 24 (2014) no. 1, pp. 29-48 | Zbl | MR | DOI

[13] Patrick L. Combettes Hilbertian convex feasibility problem: convergence of projection methods, Appl. Math. Optim., Volume 35 (1997) no. 3, pp. 311-330 | Zbl | MR | DOI

[14] Jean-Noël Corvellec; Viorica V. Motreanu Nonlinear error bounds for lower semicontinuous functions on metric spaces, Math. Program., Volume 114 (2008) no. 2, pp. 291-319 | Zbl | MR | DOI

[15] Nguyen Duy Cuong; Alexander Y. Kruger Error bounds revisited (2020) (https://arxiv.org/abs/2012.03941v1)

[16] Sien Deng Perturbation analysis of a condition number for convex inequality systems and global error bounds for analytic systems, Math. Program., Volume 83 (1998) no. 2, pp. 263-276 | Zbl | MR | DOI

[17] Asen L. Dontchev; Adrian S. Lewis; Ralph T. Rockafellar The radius of metric regularity, Trans. Am. Math. Soc., Volume 355 (2003) no. 2, pp. 493-517 | DOI | Zbl | MR

[18] Marian J. Fabian; René Henrion; Alexander Y. Kruger; Jiří V. Outrata Error bounds: necessary and sufficient conditions, Set-Valued Var. Anal., Volume 18 (2010) no. 2, pp. 121-149 | Zbl | MR | DOI

[19] Helmut Gfrerer First order and second order characterizations of metric subregularity and calmness of constraint set mappings, SIAM J. Optim., Volume 21 (2011) no. 4, pp. 1439-1474 | Zbl | MR | DOI

[20] Osman Güler Augmented Lagrangian algorithms for linear programming, J. Optim. Theory Appl., Volume 75 (1992) no. 3, pp. 445-478 | MR | DOI

[21] Robert Hesse; D. Russell Luke Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems, SIAM J. Optim., Volume 23 (2013) no. 4, pp. 2397-2419 | Zbl | MR | DOI

[22] A. J. Hoffman On approximate solutions of systems of linear inequalities, J. Res. Nat. Bur. Standards, Volume 49 (1952), pp. 263-265 | MR | DOI

[23] L. R. Huang; Kung Fu Ng On first- and second-order conditions for error bounds, SIAM J. Optim., Volume 14 (2004) no. 4, pp. 1057-1073 | MR | DOI

[24] Alexander D. Ioffe Theory of Extremal Problems, Studies in Mathematics and its Applications, 6, North-Holland, 1979

[25] Alexander D. Ioffe Metric regularity – a survey. I: Theory, J. Aust. Math. Soc., Volume 101 (2016) no. 2, pp. 188-243 | DOI | MR | Zbl

[26] Alexander D. Ioffe Metric regularity – a survey. II: Applications, J. Aust. Math. Soc., Volume 101 (2016) no. 3, pp. 376-417 | Zbl | MR | DOI

[27] Alexander D. Ioffe Variational analysis of regular mappings. Theory and applications, Springer Monographs in Mathematics, Springer, 2017 | DOI

[28] Alfredo N. Iusem; Alvaro R. De Pierro On the convergence properties of Hildreth’s quadratic programming algorithm, Math. Program., Volume 47 (1990) no. 1, pp. 37-51 | Zbl | MR | DOI

[29] Abderrahim Jourani Hoffman’s error bound, local controllability, and sensitivity analysis, SIAM J. Control Optimization, Volume 38 (2000) no. 3, pp. 947-970 | Zbl | MR | DOI

[30] Diethard Klatte; Wu Li Asymptotic constraint qualifications and global error bounds for convex inequalities, Math. Program., Volume 84 (1999) no. 1, pp. 137-160 | Zbl | MR | DOI

[31] Alexander Y. Kruger Error bounds and Hölder metric subregularity, Set-Valued Var. Anal., Volume 23 (2015) no. 4, pp. 705-736 | Zbl | DOI

[32] Alexander Y. Kruger Error bounds and metric subregularity, Optimization, Volume 64 (2015) no. 1, pp. 49-79 | DOI | Zbl | MR

[33] Alexander Y. Kruger; Marco A. López; Michel Théra Perturbation of error bounds, Math. Program., Volume 168 (2018) no. 1-2, pp. 533-554 | Zbl | MR | DOI

[34] Alexander Y. Kruger; Marco A. López; Xiaoqi Yang; Jiangxing Zhu Hölder error bounds and Hölder calmness with applications to convex semi-infinite optimization, Set-Valued Var. Anal., Volume 27 (2019) no. 4, pp. 995-1023 | Zbl | DOI

[35] Alexander Y. Kruger; Huynh Van Ngai; Michel Théra Stability of error bounds for convex constraint systems in Banach spaces, SIAM J. Optim., Volume 20 (2010) no. 6, pp. 3280-3296 | Zbl | MR | DOI

[36] Adrian S. Lewis; Jong-Shi Pang Error bounds for convex inequality systems, Generalized Convexity, Generalized Monotonicity: Recent Results (Luming, 1996) (Nonconvex Optimization and Its Applications), Volume 27, Kluwer Academic Publishers, 1996, pp. 75-100 | Zbl | DOI

[37] D. Russell Luke; H. Thao Nguyen; Matthew K. Tam Implicit error bounds for Picard iterations on Hilbert spaces, Vietnam J. Math., Volume 46 (2018) no. 2, pp. 243-258 | Zbl | MR | DOI

[38] Zhi-Quan Luo; Paul Tseng On a global error bound for a class of monotone affine variational inequality problems, Oper. Res. Lett., Volume 11 (1992) no. 3, pp. 159-165 | Zbl | MR

[39] Zhi-Quan Luo; Paul Tseng Perturbation analysis of a condition number for linear systems, SIAM J. Matrix Anal. Appl., Volume 15 (1994) no. 2, pp. 636-660 | Zbl | MR

[40] Olvi L. Mangasarian A condition number for differentiable convex inequalities, Math. Oper. Res., Volume 10 (1985), pp. 175-179 | Zbl | MR | DOI

[41] Kung Fu Ng; Xi Yin Zheng Error bounds for lower semicontinuous functions in normed spaces, SIAM J. Optim., Volume 12 (2001) no. 1, pp. 1-17 | Zbl | MR

[42] Huynh Van Ngai; Alexander Y. Kruger; Michel Théra Stability of error bounds for semi-infinite convex constraint systems, SIAM J. Optim., Volume 20 (2080) no. 4, pp. 2080-2096 | MR | DOI | Zbl

[43] Huynh Van Ngai; Michel Théra Error bounds for systems of lower semicontinuous functions in Asplund spaces, Math. Program., Volume 116 (2009) no. 1-2, pp. 397-427 | Zbl | MR | DOI

[44] Jong-Shi Pang Error bounds in mathematical programming, Math. Program., Volume 79 (1997) no. 1-3, pp. 299-332 | Zbl | MR | DOI

[45] Jean-Paul Penot Calculus without derivatives, Graduate Texts in Mathematics, 266, Springer, 2013 | DOI

[46] Robert R. Phelps Convex functions, Monotone Operators and Differentiability, Lecture Notes in Mathematics, 1364, Springer, 1993 | MR

[47] Stephen M. Robinson Bounds for error in the solution set of a perturbed linear program, Linear Algebra Appl., Volume 6 (1973), pp. 69-81 | Zbl | MR | DOI

[48] Stephen M. Robinson An application of error bounds for convex programming in a linear space, SIAM J. Control, Volume 13 (1975), pp. 271-273 | Zbl | MR | DOI

[49] Stephen M. Robinson A characterization of stability in linear programming, Oper. Res., Volume 25 (1977), pp. 435-447 | Zbl | MR | DOI

[50] Ralph T. Rockafellar Convex Analysis, Princeton Mathematical Series, 28, Princeton University Press, 1970 | DOI

[51] Paul Tseng; Dimitri P. Bertsekas On the convergence of the exponential multiplier method for convex programming, Math. Program., Volume 60 (1993) no. 1, pp. 1-19 | Zbl | MR | DOI

[52] Zili Wu; Jane J. Ye On error bounds for lower semicontinuous functions, Math. Program., Volume 92 (2002) no. 2, pp. 301-314 | Zbl | MR

[53] Xi Yin Zheng; Kung Fu Ng Perturbation analysis of error bounds for systems of conic linear inequalities in Banach spaces, SIAM J. Optim., Volume 15 (2005) no. 4, pp. 1026-1041 | Zbl | MR | DOI

[54] Xi Yin Zheng; Kung Fu Ng Metric subregularity and calmness for nonconvex generalized equations in Banach spaces, SIAM J. Optim., Volume 20 (2010) no. 5, pp. 2119-2136 | Zbl | MR | DOI

[55] Xi Yin Zheng; Kung Fu Ng Metric subregularity for proximal generalized equations in Hilbert spaces, Nonlinear Anal., Theory Methods Appl., Volume 75 (2012) no. 3, pp. 1686-1699 | Zbl | MR | DOI

[56] Xi Yin Zheng; Zhou Wei Perturbation analysis of error bounds for quasi-subsmooth inequalities and semi-infinite constraint systems, SIAM J. Optim., Volume 22 (2012) no. 1, pp. 41-65 | Zbl | MR | DOI