Sensitivity Analysis of a Stationary Point Set Map Under Total Perturbations. Part 1: Lipschitzian Stability
By applying some theorems of Levy and Mordukhovich (Math Program 99:311–327, 2004 ) and other related results, we estimate the Fréchet coderivative and the Mordukhovich coderivative of the stationary point set map of a smooth parametric optimization problem with one smooth functional constraint unde...
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| Vydané v: | Journal of optimization theory and applications Ročník 180; číslo 1; s. 91 - 116 |
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01.01.2019
Springer Nature B.V |
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| Abstract | By applying some theorems of Levy and Mordukhovich (Math Program 99:311–327,
2004
) and other related results, we estimate the Fréchet coderivative and the Mordukhovich coderivative of the stationary point set map of a smooth parametric optimization problem with one smooth functional constraint under total perturbations. From the obtained formulas, we derive necessary and sufficient conditions for the local Lipschitz-like property of the stationary point set map. This leads us to new insights into the preceding deep investigations of Levy and Mordukhovich in the above-cited paper and of Qui (J Optim Theory Appl 161:398–429,
2014
, J Glob Optim 65:615–635,
2016
). |
|---|---|
| AbstractList | By applying some theorems of Levy and Mordukhovich (Math Program 99:311–327,
2004
) and other related results, we estimate the Fréchet coderivative and the Mordukhovich coderivative of the stationary point set map of a smooth parametric optimization problem with one smooth functional constraint under total perturbations. From the obtained formulas, we derive necessary and sufficient conditions for the local Lipschitz-like property of the stationary point set map. This leads us to new insights into the preceding deep investigations of Levy and Mordukhovich in the above-cited paper and of Qui (J Optim Theory Appl 161:398–429,
2014
, J Glob Optim 65:615–635,
2016
). By applying some theorems of Levy and Mordukhovich (Math Program 99:311–327, 2004) and other related results, we estimate the Fréchet coderivative and the Mordukhovich coderivative of the stationary point set map of a smooth parametric optimization problem with one smooth functional constraint under total perturbations. From the obtained formulas, we derive necessary and sufficient conditions for the local Lipschitz-like property of the stationary point set map. This leads us to new insights into the preceding deep investigations of Levy and Mordukhovich in the above-cited paper and of Qui (J Optim Theory Appl 161:398–429, 2014, J Glob Optim 65:615–635, 2016). |
| Author | Huyen, Duong Thi Kim Yao, Jen-Chih Yen, Nguyen Dong |
| Author_xml | – sequence: 1 givenname: Duong Thi Kim surname: Huyen fullname: Huyen, Duong Thi Kim organization: Graduate Training Center, Institute of Mathematics, Vietnam Academy of Science and Technology – sequence: 2 givenname: Jen-Chih surname: Yao fullname: Yao, Jen-Chih organization: Center for General Education, China Medical University – sequence: 3 givenname: Nguyen Dong surname: Yen fullname: Yen, Nguyen Dong email: ndyen@math.ac.vn organization: Institute of Mathematics, Vietnam Academy of Science and Technology |
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| Cites_doi | 10.1080/00036811.2010.483432 10.1287/moor.2014.0669 10.1137/060658576 10.1007/s10957-013-0427-0 10.1137/15M1036890 10.1137/090766413 10.1287/moor.1070.0297 10.1007/3-540-31246-3 10.1287/moor.9.1.87 10.1080/02331934.2014.979819 10.1007/978-0-387-87821-8 10.1016/j.na.2010.06.007 10.1007/s10898-015-0387-z 10.1016/0362-546X(89)90083-7 10.1137/120887722 10.1007/s11590-015-0915-2 10.1137/120882329 10.1016/j.na.2010.10.039 10.1137/140998469 10.1007/s10957-011-9937-9 10.1137/S1052623495284029 10.1137/110852528 10.1007/978-3-642-02431-3 10.1016/j.jmaa.2011.02.006 10.1016/0022-247X(88)90034-0 10.1090/S0002-9947-1993-1156300-4 10.1137/0713043 10.1137/16M1086881 10.1137/130906878 10.1016/j.na.2008.04.005 10.1137/120868657 10.1007/s10107-003-0452-0 10.1016/j.na.2013.09.007 |
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| Keywords | 90C31 90C20 Lipschitz-like property 49J53 49K40 Coderivative Smooth functional constraint Smooth parametric optimization problem Stationary point set map |
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| References | Célia, Alain (CR9) 2005; 39 Qui (CR29) 2011; 381 Yao, Yen (CR33) 2009; 5 Lu, Robinson (CR25) 2008; 33 Mordukhovich (CR8) 1993; 340 Huyen, Yen (CR37) 2016; 26 Dontchev, Rockafellar (CR23) 1996; 6 Yao, Yen (CR32) 2009; 34 Rudin (CR39) 1976 Levy, Mordukhovich (CR1) 2004; 99 Qui (CR4) 2014; 161 Lee, Yen (CR3) 2011; 90 Aubin (CR5) 1984; 9 Gfrerer, Mordukhovich (CR13) 2017; 27 Mordukhovich, Nghia, Rockafellar (CR20) 2015; 40 Nam (CR26) 2010; 73 Yen, Yao (CR2) 2009; 70 Qui (CR28) 2011; 74 Trang (CR31) 2016; 10 Borwein, Zhuang (CR6) 1988; 134 Rockafellar, Wets (CR14) 1998 Qui, Yen (CR17) 2014; 24 Dontchev, Rockafellar (CR11) 2009 Mordukhovich, Rockafellar, Sarabi (CR21) 2013; 23 Guo, Lin, Ye (CR35) 2012; 22 Ban, Song (CR22) 2016; 65 Mordukhovich, Nghia (CR18) 2014; 24 Mordukhovich (CR36) 2006 Qui (CR15) 2016; 65 Robinson (CR30) 2007; 18 Penot (CR7) 1989; 13 Dontchev (CR10) 1996; 22 Robinson (CR12) 1976; 13 Qui (CR34) 2012; 153 Mordukhovich, Nghia (CR19) 2016; 26 Henrion, Mordukhovich, Nam (CR24) 2010; 20 Lee, Yen (CR16) 2014; 95 Mordukhovich, Rockafellar (CR38) 2012; 22 Qui (CR27) 2011; 36 AL Dontchev (1294_CR10) 1996; 22 DTK Huyen (1294_CR37) 2016; 26 GM Lee (1294_CR16) 2014; 95 NT Qui (1294_CR29) 2011; 381 JM Borwein (1294_CR6) 1988; 134 S Lu (1294_CR25) 2008; 33 L Guo (1294_CR35) 2012; 22 J-C Yao (1294_CR33) 2009; 5 NM Nam (1294_CR26) 2010; 73 J-P Aubin (1294_CR5) 1984; 9 BS Mordukhovich (1294_CR36) 2006 BS Mordukhovich (1294_CR8) 1993; 340 H Gfrerer (1294_CR13) 2017; 27 AB Levy (1294_CR1) 2004; 99 R Henrion (1294_CR24) 2010; 20 J-P Penot (1294_CR7) 1989; 13 SM Robinson (1294_CR12) 1976; 13 SM Robinson (1294_CR30) 2007; 18 J-C Yao (1294_CR32) 2009; 34 A Dontchev (1294_CR11) 2009 J-A Célia (1294_CR9) 2005; 39 NT Qui (1294_CR17) 2014; 24 BS Mordukhovich (1294_CR21) 2013; 23 NTQ Trang (1294_CR31) 2016; 10 GM Lee (1294_CR3) 2011; 90 BS Mordukhovich (1294_CR20) 2015; 40 NT Qui (1294_CR27) 2011; 36 NT Qui (1294_CR28) 2011; 74 L Ban (1294_CR22) 2016; 65 AL Dontchev (1294_CR23) 1996; 6 NT Qui (1294_CR34) 2012; 153 NT Qui (1294_CR4) 2014; 161 NT Qui (1294_CR15) 2016; 65 RT Rockafellar (1294_CR14) 1998 BS Mordukhovich (1294_CR19) 2016; 26 ND Yen (1294_CR2) 2009; 70 W Rudin (1294_CR39) 1976 BS Mordukhovich (1294_CR18) 2014; 24 BS Mordukhovich (1294_CR38) 2012; 22 |
| References_xml | – volume: 90 start-page: 1011 year: 2011 end-page: 1027 ident: CR3 article-title: Fréchet and normal coderivatives of implicit multifunctions publication-title: Appl. Anal. doi: 10.1080/00036811.2010.483432 – volume: 40 start-page: 226 year: 2015 end-page: 252 ident: CR20 article-title: Full stability in finite-dimensional optimization: Mordukhovich publication-title: Math. Oper. Res. doi: 10.1287/moor.2014.0669 – volume: 34 start-page: 157 year: 2009 end-page: 172 ident: CR32 article-title: Coderivative calculation related to a parametric affine variational inequality, Part 1: Basic calculations publication-title: Acta Math. Vietnam – volume: 18 start-page: 1046 year: 2007 end-page: 1060 ident: CR30 article-title: Solution continuity in monotone affine variational inequalities publication-title: SIAM J. Optim. doi: 10.1137/060658576 – volume: 5 start-page: 493 year: 2009 end-page: 506 ident: CR33 article-title: Coderivative calculation related to a parametric affine variational inequality, Part 2: Applications publication-title: Pacific J. Optim. – volume: 161 start-page: 398 year: 2014 end-page: 429 ident: CR4 article-title: Generalized differentiation of a class of normal cone operators publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-013-0427-0 – volume: 26 start-page: 1032 year: 2016 end-page: 1059 ident: CR19 article-title: Local monotonicity and full stability for parametric variational systems publication-title: SIAM J. Optim. doi: 10.1137/15M1036890 – volume: 20 start-page: 2199 year: 2010 end-page: 2227 ident: CR24 article-title: Second-oder analysis of polyhedral systems in finite and infinite dimensions and applications to robust stability of variational inequalities publication-title: SIAM J. Optim. doi: 10.1137/090766413 – volume: 33 start-page: 689 year: 2008 end-page: 711 ident: CR25 article-title: Variational inequalities over perturbed polyhedral convex sets publication-title: Math. Oper. Res. doi: 10.1287/moor.1070.0297 – year: 2006 ident: CR36 publication-title: Variational Analysis and Generalized Differentiation, Vol. I: Basic Theory, Vol. II: Applications doi: 10.1007/3-540-31246-3 – volume: 9 start-page: 87 year: 1984 end-page: 111 ident: CR5 article-title: Lipschitz behavior of solutions to convex minimization problems publication-title: Math. Oper. Res. doi: 10.1287/moor.9.1.87 – volume: 65 start-page: 9 year: 2016 end-page: 34 ident: CR22 article-title: Linearly perturbed generalized polyhedral normal cone mappings and applications publication-title: Optimization doi: 10.1080/02331934.2014.979819 – year: 2009 ident: CR11 publication-title: Implicit Functions and Solution Mappings. A View from Variational Analysis doi: 10.1007/978-0-387-87821-8 – volume: 22 start-page: 283 year: 1996 end-page: 296 ident: CR10 article-title: Uniform convergence of the Newton method for Aubin continuous maps. Well-posedness and stability of variational problems publication-title: Serdica Math. J. – volume: 73 start-page: 2271 year: 2010 end-page: 2282 ident: CR26 article-title: Coderivatives of normal cone mappings and Lipschitzian stability of parametric variational inequalities publication-title: Nonlinear Anal. doi: 10.1016/j.na.2010.06.007 – volume: 65 start-page: 615 year: 2016 end-page: 635 ident: CR15 article-title: Coderivatives of implicit multifunctions and stability of variational systems publication-title: J. Glob. Optim. doi: 10.1007/s10898-015-0387-z – volume: 13 start-page: 629 year: 1989 end-page: 643 ident: CR7 article-title: Metric regularity, openness and Lipschitzian behavior of multifunctions publication-title: Nonlinear Anal. doi: 10.1016/0362-546X(89)90083-7 – volume: 23 start-page: 1810 year: 2013 end-page: 1849 ident: CR21 article-title: Characterizations of full stability in constrained optimization publication-title: SIAM J. Optim. doi: 10.1137/120887722 – volume: 10 start-page: 1221 year: 2016 end-page: 1231 ident: CR31 article-title: A note on Lipschitzian stability of variational inequalities over perturbed polyhedral convex sets publication-title: Optim. Lett. doi: 10.1007/s11590-015-0915-2 – volume: 24 start-page: 210 year: 2014 end-page: 231 ident: CR17 article-title: A class of linear generalized equations publication-title: SIAM J. Optim. doi: 10.1137/120882329 – volume: 74 start-page: 1676 year: 2011 end-page: 1689 ident: CR28 article-title: Linearly perturbed polyhedral normal cone mappings and applications publication-title: Nonlinear Anal. doi: 10.1016/j.na.2010.10.039 – volume: 26 start-page: 986 year: 2016 end-page: 1007 ident: CR37 article-title: Coderivatives and the solution map of a linear constraint system publication-title: SIAM J. Optim. doi: 10.1137/140998469 – year: 1976 ident: CR39 publication-title: Principles of Mathematical Analysis – volume: 39 start-page: 97 year: 2005 end-page: 112 ident: CR9 article-title: A variant of Newton’s method for generalized equations publication-title: Rev. Colombiana Mat. – volume: 153 start-page: 98 year: 2012 end-page: 122 ident: CR34 article-title: Nonlinear perturbations of polyhedral normal cone mappings and affine variational inequalities publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-011-9937-9 – volume: 6 start-page: 1087 year: 1996 end-page: 1105 ident: CR23 article-title: Characterizations of strong regularity for variational inequalities over polyhedral convex sets publication-title: SIAM J. Optim. doi: 10.1137/S1052623495284029 – volume: 36 start-page: 601 year: 2011 end-page: 610 ident: CR27 article-title: Upper and lower estimates for a Fréchet normal cone publication-title: Acta Math. Vietnam – volume: 22 start-page: 953 year: 2012 end-page: 986 ident: CR38 article-title: Second-order subdifferential calculus with applications to tilt stability in optimization publication-title: SIAM J. Optim. doi: 10.1137/110852528 – year: 1998 ident: CR14 publication-title: Variational Analysis doi: 10.1007/978-3-642-02431-3 – volume: 381 start-page: 352 year: 2011 end-page: 364 ident: CR29 article-title: New results on linearly perturbed polyhedral normal cone mappings publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2011.02.006 – volume: 134 start-page: 441 year: 1988 end-page: 459 ident: CR6 article-title: Verifiable necessary and sufficient conditions for regularity of set-valued and single-valued maps publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(88)90034-0 – volume: 340 start-page: 1 year: 1993 end-page: 36 ident: CR8 article-title: Complete characterization of openness, metric regularity, and Lipschitzian properties of multifunctions publication-title: Trans. Am. Math. Soc. doi: 10.1090/S0002-9947-1993-1156300-4 – volume: 13 start-page: 497 year: 1976 end-page: 513 ident: CR12 article-title: Stability theory for systems of inequalities, II. Differentiable nonlinear systems publication-title: SIAM J. Numer. Anal. doi: 10.1137/0713043 – volume: 27 start-page: 438 year: 2017 end-page: 465 ident: CR13 article-title: Robinson stability of parametric constraint systems via variational analysis publication-title: SIAM J. Optim. doi: 10.1137/16M1086881 – volume: 24 start-page: 1344 year: 2014 end-page: 1381 ident: CR18 article-title: Full Lipschitzian and Hölderian stability in optimization with applications to mathematical programming and optimal control publication-title: SIAM J. Optim. doi: 10.1137/130906878 – volume: 70 start-page: 2806 year: 2009 end-page: 2815 ident: CR2 article-title: Point-based sufficient conditions for metric regularity of implicit multifunctions publication-title: Nonlinear Anal. doi: 10.1016/j.na.2008.04.005 – volume: 22 start-page: 1151 year: 2012 end-page: 1176 ident: CR35 article-title: Stability analysis for parametric mathematical programs with geometric constraints and its applications publication-title: SIAM J. Optim. doi: 10.1137/120868657 – volume: 99 start-page: 311 year: 2004 end-page: 327 ident: CR1 article-title: Coderivatives in parametric optimization publication-title: Math. Program. doi: 10.1007/s10107-003-0452-0 – volume: 95 start-page: 191 year: 2014 end-page: 201 ident: CR16 article-title: Coderivatives of a Karush-Kuhn-Tucker point set map and applications publication-title: Nonlinear Anal. doi: 10.1016/j.na.2013.09.007 – volume: 73 start-page: 2271 year: 2010 ident: 1294_CR26 publication-title: Nonlinear Anal. doi: 10.1016/j.na.2010.06.007 – volume-title: Principles of Mathematical Analysis year: 1976 ident: 1294_CR39 – volume: 95 start-page: 191 year: 2014 ident: 1294_CR16 publication-title: Nonlinear Anal. doi: 10.1016/j.na.2013.09.007 – volume: 22 start-page: 283 year: 1996 ident: 1294_CR10 publication-title: Serdica Math. J. – volume: 22 start-page: 953 year: 2012 ident: 1294_CR38 publication-title: SIAM J. Optim. doi: 10.1137/110852528 – volume: 340 start-page: 1 year: 1993 ident: 1294_CR8 publication-title: Trans. Am. Math. Soc. doi: 10.1090/S0002-9947-1993-1156300-4 – volume-title: Variational Analysis year: 1998 ident: 1294_CR14 doi: 10.1007/978-3-642-02431-3 – volume: 26 start-page: 986 year: 2016 ident: 1294_CR37 publication-title: SIAM J. Optim. doi: 10.1137/140998469 – volume: 74 start-page: 1676 year: 2011 ident: 1294_CR28 publication-title: Nonlinear Anal. doi: 10.1016/j.na.2010.10.039 – volume: 99 start-page: 311 year: 2004 ident: 1294_CR1 publication-title: Math. Program. doi: 10.1007/s10107-003-0452-0 – volume: 13 start-page: 497 year: 1976 ident: 1294_CR12 publication-title: SIAM J. Numer. Anal. doi: 10.1137/0713043 – volume: 23 start-page: 1810 year: 2013 ident: 1294_CR21 publication-title: SIAM J. Optim. doi: 10.1137/120887722 – volume: 65 start-page: 9 year: 2016 ident: 1294_CR22 publication-title: Optimization doi: 10.1080/02331934.2014.979819 – volume: 65 start-page: 615 year: 2016 ident: 1294_CR15 publication-title: J. Glob. Optim. doi: 10.1007/s10898-015-0387-z – volume: 24 start-page: 210 year: 2014 ident: 1294_CR17 publication-title: SIAM J. Optim. doi: 10.1137/120882329 – volume: 39 start-page: 97 year: 2005 ident: 1294_CR9 publication-title: Rev. Colombiana Mat. – volume: 27 start-page: 438 year: 2017 ident: 1294_CR13 publication-title: SIAM J. Optim. doi: 10.1137/16M1086881 – volume: 34 start-page: 157 year: 2009 ident: 1294_CR32 publication-title: Acta Math. Vietnam – volume: 20 start-page: 2199 year: 2010 ident: 1294_CR24 publication-title: SIAM J. Optim. doi: 10.1137/090766413 – volume: 70 start-page: 2806 year: 2009 ident: 1294_CR2 publication-title: Nonlinear Anal. doi: 10.1016/j.na.2008.04.005 – volume: 24 start-page: 1344 year: 2014 ident: 1294_CR18 publication-title: SIAM J. Optim. doi: 10.1137/130906878 – volume: 33 start-page: 689 year: 2008 ident: 1294_CR25 publication-title: Math. Oper. Res. doi: 10.1287/moor.1070.0297 – volume: 10 start-page: 1221 year: 2016 ident: 1294_CR31 publication-title: Optim. Lett. doi: 10.1007/s11590-015-0915-2 – volume: 153 start-page: 98 year: 2012 ident: 1294_CR34 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-011-9937-9 – volume: 18 start-page: 1046 year: 2007 ident: 1294_CR30 publication-title: SIAM J. Optim. doi: 10.1137/060658576 – volume: 26 start-page: 1032 year: 2016 ident: 1294_CR19 publication-title: SIAM J. Optim. doi: 10.1137/15M1036890 – volume: 90 start-page: 1011 year: 2011 ident: 1294_CR3 publication-title: Appl. Anal. doi: 10.1080/00036811.2010.483432 – volume-title: Implicit Functions and Solution Mappings. A View from Variational Analysis year: 2009 ident: 1294_CR11 doi: 10.1007/978-0-387-87821-8 – volume-title: Variational Analysis and Generalized Differentiation, Vol. I: Basic Theory, Vol. II: Applications year: 2006 ident: 1294_CR36 doi: 10.1007/3-540-31246-3 – volume: 9 start-page: 87 year: 1984 ident: 1294_CR5 publication-title: Math. Oper. Res. doi: 10.1287/moor.9.1.87 – volume: 6 start-page: 1087 year: 1996 ident: 1294_CR23 publication-title: SIAM J. Optim. doi: 10.1137/S1052623495284029 – volume: 36 start-page: 601 year: 2011 ident: 1294_CR27 publication-title: Acta Math. Vietnam – volume: 381 start-page: 352 year: 2011 ident: 1294_CR29 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2011.02.006 – volume: 22 start-page: 1151 year: 2012 ident: 1294_CR35 publication-title: SIAM J. Optim. doi: 10.1137/120868657 – volume: 40 start-page: 226 year: 2015 ident: 1294_CR20 publication-title: Math. Oper. Res. doi: 10.1287/moor.2014.0669 – volume: 5 start-page: 493 year: 2009 ident: 1294_CR33 publication-title: Pacific J. Optim. – volume: 161 start-page: 398 year: 2014 ident: 1294_CR4 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-013-0427-0 – volume: 134 start-page: 441 year: 1988 ident: 1294_CR6 publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(88)90034-0 – volume: 13 start-page: 629 year: 1989 ident: 1294_CR7 publication-title: Nonlinear Anal. doi: 10.1016/0362-546X(89)90083-7 |
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| Snippet | By applying some theorems of Levy and Mordukhovich (Math Program 99:311–327,
2004
) and other related results, we estimate the Fréchet coderivative and the... By applying some theorems of Levy and Mordukhovich (Math Program 99:311–327, 2004) and other related results, we estimate the Fréchet coderivative and the... |
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| SubjectTerms | Applications of Mathematics Calculus of Variations and Optimal Control; Optimization Engineering Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Sensitivity analysis Theory of Computation |
| Title | Sensitivity Analysis of a Stationary Point Set Map Under Total Perturbations. Part 1: Lipschitzian Stability |
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