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Volumn 93, Issue 1, 1997, Pages 199-225

Stability of the solution set of perturbed nonsmooth inequality systems and application

Author keywords

Generalized inequality systems; Generalized Jacobians; Locally Lipschitz vector valued functions; Optimal value functions

Indexed keywords

STABILITY;

EID: 0031519907     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022662120550     Document Type: Article
Times cited : (27)

References (32)
  • 3
    • 0016993914 scopus 로고
    • Stability theory for systems of inequalities, part 2: Differentiable nonlinear systems
    • ROBINSON, S. M., Stability Theory for Systems of Inequalities, Part 2: Differentiable Nonlinear Systems, SIAM Journal on Numerical Analysis, Vol. 13, pp. 497-513, 1976.
    • (1976) SIAM Journal on Numerical Analysis , vol.13 , pp. 497-513
    • Robinson, S.M.1
  • 4
    • 0040821342 scopus 로고
    • Stability, surjectivity, and local invertibility of nondifferentiable mappings
    • DUONG, P. C., and TUY, H., Stability, Surjectivity, and Local Invertibility of Nondifferentiable Mappings, Acta Mathematica Vietnamica, Vol. 3, pp. 89-105, 1978.
    • (1978) Acta Mathematica Vietnamica , vol.3 , pp. 89-105
    • Duong, P.C.1    Tuy, H.2
  • 5
    • 0002800189 scopus 로고
    • Regularity and stability for the mathematical programming problem in Banach space
    • ZOWE, J., and KURCYUSZ, S., Regularity and Stability for the Mathematical Programming Problem in Banach Space, Applied Mathematics and Optimization, Vol. 5, pp. 49-62, 1979.
    • (1979) Applied Mathematics and Optimization , vol.5 , pp. 49-62
    • Zowe, J.1    Kurcyusz, S.2
  • 6
    • 0020166920 scopus 로고
    • Differential properties of the marginal function in mathematical programming
    • GAUVIN, J., and DUBEAU, F., Differential Properties of the Marginal Function in Mathematical Programming, Mathematical Programming Study, Vol. 19, pp. 101-119, 1982.
    • (1982) Mathematical Programming Study , vol.19 , pp. 101-119
    • Gauvin, J.1    Dubeau, F.2
  • 7
    • 0002789370 scopus 로고
    • Lagrange multipliers and subderivatives of optimal value functions in nonlinear programming
    • ROCKAFELLAR, R. T., Lagrange Multipliers and Subderivatives of Optimal Value Functions in Nonlinear Programming, Mathematical Programming Study, Vol. 17, pp. 28-66, 1982.
    • (1982) Mathematical Programming Study , vol.17 , pp. 28-66
    • Rockafellar, R.T.1
  • 8
    • 0003859933 scopus 로고
    • John Wiley and Sons, Wiley-Interscience, New York, New York
    • CLARKE, F. H., Optimization and Nonsmooth Analysis, John Wiley and Sons, Wiley-Interscience, New York, New York, 1983.
    • (1983) Optimization and Nonsmooth Analysis
    • Clarke, F.H.1
  • 9
    • 0021375867 scopus 로고
    • Lipschitz behavior of solutions to convex minimization problems
    • AUBIN, J. P., Lipschitz Behavior of Solutions to Convex Minimization Problems, Mathematics of Operations Research, Vol. 9, pp. 87-111, 1984.
    • (1984) Mathematics of Operations Research , vol.9 , pp. 87-111
    • Aubin, J.P.1
  • 14
    • 0026220036 scopus 로고
    • On the stability of sets defined by a finite number of equalities and inequalities
    • BONNANS, J. F., and LAUNAY, G., On the Stability of Sets Defined by a Finite Number of Equalities and Inequalities, Journal of Optimization Theory and Applications, Vol. 70, pp. 417-428, 1991.
    • (1991) Journal of Optimization Theory and Applications , vol.70 , pp. 417-428
    • Bonnans, J.F.1    Launay, G.2
  • 15
    • 0000928277 scopus 로고
    • Approximations and metric regularity in mathematical programming in Banach spaces
    • JOURANI, A., and THIBAULT, L., Approximations and Metric Regularity in Mathematical Programming in Banach Spaces, Mathematics of Operations Research, Vol. 18, pp. 390-401, 1993.
    • (1993) Mathematics of Operations Research , vol.18 , pp. 390-401
    • Jourani, A.1    Thibault, L.2
  • 16
    • 84966250815 scopus 로고
    • Complete characterization of openness, metric regularity, and lipschitzian properties of multifunctions
    • MORDUKHOVICH, B., Complete Characterization of Openness, Metric Regularity, and Lipschitzian Properties of Multifunctions, Transactions of the American Mathematical Society, Vol. 340, pp. 1-36, 1993.
    • (1993) Transactions of the American Mathematical Society , vol.340 , pp. 1-36
    • Mordukhovich, B.1
  • 17
    • 0001158218 scopus 로고
    • Lipschitzian stability of constraint systems and generalized equations
    • MORDUKHOVICH, B., Lipschitzian Stability of Constraint Systems and Generalized Equations, Nonlinear Analysis, Vol. 22, pp. 173-206, 1994.
    • (1994) Nonlinear Analysis , vol.22 , pp. 173-206
    • Mordukhovich, B.1
  • 18
    • 0000948820 scopus 로고
    • Implicit functions, lipschitz maps, and stability in optimization
    • DONTCHEV, A. L., and HARGER, W. W., Implicit Functions, Lipschitz Maps, and Stability in Optimization, Mathematics of Operations Research, Vol. 19, pp. 753-768, 1994.
    • (1994) Mathematics of Operations Research , vol.19 , pp. 753-768
    • Dontchev, A.L.1    Harger, W.W.2
  • 19
    • 0028449086 scopus 로고
    • Constraint qualifications and lagrange multipliers in nondifferentiable programming problems
    • JOURANI, A., Constraint Qualifications and Lagrange Multipliers in Nondifferentiable Programming Problems, Journal of Optimization Theory and Applications, Vol. 81, pp. 533-548, 1994.
    • (1994) Journal of Optimization Theory and Applications , vol.81 , pp. 533-548
    • Jourani, A.1
  • 21
    • 0040226654 scopus 로고
    • Implicit function theorems for set-valued maps
    • YEN, N. D., Implicit Function Theorems for Set-Valued Maps, Acta Mathematica Vietnamica, Vol. 12, pp. 17-28, 1987.
    • (1987) Acta Mathematica Vietnamica , vol.12 , pp. 17-28
    • Yen, N.D.1
  • 22
    • 0002583747 scopus 로고
    • On implicit function theorems for set-valued maps and their applications to mathematical programming under inclusion constraints
    • DIEN, P. H., and YEN, N. D., On Implicit Function Theorems for Set-Valued Maps and Their Applications to Mathematical Programming under Inclusion Constraints, Applied Mathematics and Optimization, Vol. 24, pp. 35-54, 1991.
    • (1991) Applied Mathematics and Optimization , vol.24 , pp. 35-54
    • Dien, P.H.1    Yen, N.D.2
  • 24
    • 0040226652 scopus 로고
    • Comportement lipschitzien des solutions de problèmes de minimisation convexes
    • Paris
    • AUBIN, J. P., Comportement Lipschitzien des Solutions de Problèmes de Minimisation Convexes, Comptes Rendus de l'Academie des Sciences, Paris, Vol. 295, pp. 235-238, 1982.
    • (1982) Comptes Rendus de l'Academie des Sciences , vol.295 , pp. 235-238
    • Aubin, J.P.1
  • 25
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton, New Jersey
    • ROCKAFELLAR, R. T., Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 26
    • 49949133603 scopus 로고
    • The Fritz-John necessary optimality conditions in the presence of equality and inequality constraints
    • MANGASARIAN, O. L., and FROMOVITZ, S., The Fritz-John Necessary Optimality Conditions in the Presence of Equality and Inequality Constraints, Journal of Mathematical Analysis and Applications, Vol. 17, pp. 37-47, 1967.
    • (1967) Journal of Mathematical Analysis and Applications , vol.17 , pp. 37-47
    • Mangasarian, O.L.1    Fromovitz, S.2
  • 27
    • 0040226655 scopus 로고
    • Differentiability of set-valued maps in Banach spaces
    • SACH, P. H., Differentiability of Set-Valued Maps in Banach Spaces, Mathematische Nachrichten, Vol. 139, pp. 215-235, 1988.
    • (1988) Mathematische Nachrichten , vol.139 , pp. 215-235
    • Sach, P.H.1
  • 28
    • 0026852251 scopus 로고
    • Error bounds for generalized lagrange multipliers in locally lipschitz programming
    • PAPPALARDO, M., Error Bounds for Generalized Lagrange Multipliers in Locally Lipschitz Programming, Journal of Optimization Theory and Applications, Vol. 73, pp. 205-210, 1992.
    • (1992) Journal of Optimization Theory and Applications , vol.73 , pp. 205-210
    • Pappalardo, M.1
  • 31
    • 38249025950 scopus 로고
    • Metric regularity, openness, and lipschitzian behavior of multifunctions
    • PENOT, J. P., Metric Regularity, Openness, and Lipschitzian Behavior of Multifunctions, Nonlinear Analysis, Vol. 13, pp. 629-643, 1989.
    • (1989) Nonlinear Analysis , vol.13 , pp. 629-643
    • Penot, J.P.1
  • 32
    • 0028406398 scopus 로고
    • Image of a parametric optimization problem and continuity of the perturbation function
    • MASTROENI, M., PAPPALARDO, P., and YEN, N. D., Image of a Parametric Optimization Problem and Continuity of the Perturbation Function, Journal of Optimization Theory and Applications, Vol. 81, pp. 193-202, 1994.
    • (1994) Journal of Optimization Theory and Applications , vol.81 , pp. 193-202
    • Mastroeni, M.1    Pappalardo, P.2    Yen, N.D.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.