메뉴 건너뛰기




Volumn 13, Issue 1-3, 1999, Pages 61-85

Generalized Kojima-Functions and Lipschitz Stability of Critical Points

Author keywords

Critical points; Kojima functions; Lipschitz stability; Mangasarian Fromovitz constraint qualification; Regularity; Stationary solutions

Indexed keywords


EID: 0001932723     PISSN: 09266003     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1008648605071     Document Type: Article
Times cited : (15)

References (40)
  • 2
    • 0041528119 scopus 로고    scopus 로고
    • Optimization problems with perturbations, a guided tour
    • to appear revised manuscript February
    • F. Bonnans and A. Shapiro, "Optimization problems with perturbations, a guided tour," SIAM Review, to appear (revised manuscript February, 1997).
    • (1997) SIAM Review
    • Bonnans, F.1    Shapiro, A.2
  • 3
    • 56049086689 scopus 로고
    • On the inverse function theorem
    • F. Clarke, "On the inverse function theorem," Pacific Journ. Math., vol 64, pp. 97-102, 1976.
    • (1976) Pacific Journ. Math. , vol.64 , pp. 97-102
    • Clarke, F.1
  • 5
    • 0000948820 scopus 로고
    • Implicit functions, Lipschitz maps, and stability in optimization
    • A. Dontchev and W.W. Hager, "Implicit functions, Lipschitz maps, and stability in optimization," Math. Oper. Res., vol. 19, pp. 753-768, 1994.
    • (1994) Math. Oper. Res. , vol.19 , pp. 753-768
    • Dontchev, A.1    Hager, W.W.2
  • 6
    • 0030521635 scopus 로고    scopus 로고
    • Characterizations of strong regularity for variational inequalities over polyhedral convex sets
    • A. Dontchev and R.T. Rockafellar, "Characterizations of strong regularity for variational inequalities over polyhedral convex sets," SIAM Journal on Optimization, vol. 6, pp. 1087-1105, 1996.
    • (1996) SIAM Journal on Optimization , vol.6 , pp. 1087-1105
    • Dontchev, A.1    Rockafellar, R.T.2
  • 7
    • 0002128319 scopus 로고    scopus 로고
    • Characterizations of Lipschitz stability in nonlinear programming
    • A.V. Fiacco, Ed., Marcel Dekker: New York
    • A. Dontchev and R.T. Rockafellar, "Characterizations of Lipschitz stability in nonlinear programming," in Mathematical Programming with Data Perturbations (A.V. Fiacco, Ed.), Marcel Dekker: New York, pp.65-82, 1997.
    • (1997) Mathematical Programming with Data Perturbations , pp. 65-82
    • Dontchev, A.1    Rockafellar, R.T.2
  • 11
    • 0025517299 scopus 로고
    • Implicit functions and sensitivity of stationary points
    • H. Th. Jongen, D. Klatte and K. Tammer, "Implicit functions and sensitivity of stationary points," Math. Programming, vol. 49, pp. 123-138, 1990.
    • (1990) Math. Programming , vol.49 , pp. 123-138
    • Jongen, H.Th.1    Klatte, D.2    Tammer, K.3
  • 12
    • 0022807389 scopus 로고
    • On iterated minimization in nonconvex optimization
    • H.Th. Jongen, T. Möbert, and K. Tammer, "On iterated minimization in nonconvex optimization," Math. Oper. Res., vol. 11, pp. 679-691, 1986.
    • (1986) Math. Oper. Res. , vol.11 , pp. 679-691
    • Jongen, H.Th.1    Möbert, T.2    Tammer, K.3
  • 13
    • 0042029276 scopus 로고
    • On sufficient conditions for local optimality in semi-infinite programming
    • H. Th. Jongen, W. Wetterling and G. Zwier, "On sufficient conditions for local optimality in semi-infinite programming," Optimization, vol. 18, pp. 165-178, 1987.
    • (1987) Optimization , vol.18 , pp. 165-178
    • Jongen, H.Th.1    Wetterling, W.2    Zwier, G.3
  • 14
    • 34249843405 scopus 로고
    • Sensitivity analysis for nonsmooth generalized equations
    • A. King and R.T. Rockafellar, "Sensitivity analysis for nonsmooth generalized equations," Math. Programming, vol. 55, pp. 341-364, 1992.
    • (1992) Math. Programming , vol.55 , pp. 341-364
    • King, A.1    Rockafellar, R.T.2
  • 16
    • 0043031017 scopus 로고
    • Stability of stationary solutions in semi-infinite optimization via the reduction approach
    • W. Oettli and D. Pallaschke, Eds., Springer: Berlin
    • D. Klatte, "Stability of stationary solutions in semi-infinite optimization via the reduction approach," in Advances in Optimization (W. Oettli and D. Pallaschke, Eds.), Springer: Berlin, pp. 155-170, 1992.
    • (1992) Advances in Optimization , pp. 155-170
    • Klatte, D.1
  • 17
    • 0042530068 scopus 로고    scopus 로고
    • Strong stability in nonlinear programming revisited
    • to appear, revised manuscript December
    • D. Klatte and B. Kummer, "Strong stability in nonlinear programming revisited", J. Austral. Math. Soc., to appear, revised manuscript December 1997.
    • (1997) J. Austral. Math. Soc.
    • Klatte, D.1    Kummer, B.2
  • 18
    • 0002177145 scopus 로고
    • Strong stability of stationary solutions and Karush-Kuhn-Tucker points in nonlinear optimization
    • D. Klatte and K. Tammer, "Strong stability of stationary solutions and Karush-Kuhn-Tucker points in nonlinear optimization," Annals of Oper. Res., vol. 27, pp. 285-308, 1990.
    • (1990) Annals of Oper. Res. , vol.27 , pp. 285-308
    • Klatte, D.1    Tammer, K.2
  • 19
    • 0002416157 scopus 로고
    • Strongly stable stationary solutions in nonlinear programs
    • S.M. Robinson, Ed., Academic Press: New York
    • M. Kojima, "Strongly stable stationary solutions in nonlinear programs," in Analysis and Computation of Fixed Points (S.M. Robinson, Ed.), Academic Press: New York, pp. 93-138, 1980.
    • (1980) Analysis and Computation of Fixed Points , pp. 93-138
    • Kojima, M.1
  • 23
    • 0001472237 scopus 로고
    • Newton's method based on generalized derivatives for nonsmooth functions: Convergence analysis
    • W. Oettli and D. Pallaschke, Eds., Springer: Berlin
    • B. Kummer, "Newton's method based on generalized derivatives for nonsmooth functions: convergence analysis," in Advances in Optimization (W. Oettli and D. Pallaschke, Eds.), Springer: Berlin, pp. 171-194, 1992.
    • (1992) Advances in Optimization , pp. 171-194
    • Kummer, B.1
  • 24
    • 0012281556 scopus 로고    scopus 로고
    • Lipschitzian and pseudo-Lipschitzian inverse functions and applications to nonlinear Programming
    • A.V. Fiacco, Ed., Marcel Dekker: New York
    • B. Kummer, "Lipschitzian and pseudo-Lipschitzian inverse functions and applications to nonlinear Programming," in Mathematical Programming with Data Perturbations (A.V. Fiacco, Ed.), Marcel Dekker: New York, pp.201-222, 1997.
    • (1997) Mathematical Programming with Data Perturbations , pp. 201-222
    • Kummer, B.1
  • 25
    • 0008693608 scopus 로고    scopus 로고
    • Implicit multifunction theorems for the sensitivity analysis of variational conditions
    • A.B. Levy, "Implicit multifunction theorems for the sensitivity analysis of variational conditions," Math. Programming, vol. 74, pp. 333-350, 1996.
    • (1996) Math. Programming , vol.74 , pp. 333-350
    • Levy, A.B.1
  • 26
    • 0043031019 scopus 로고    scopus 로고
    • Errata in application section of [3]
    • to appear
    • A.B. Levy, "Errata in application section of [3]," Math. Programming, to appear.
    • Math. Programming
    • Levy, A.B.1
  • 27
    • 0002727212 scopus 로고
    • Sensitivity of solutions in nonlinear programs with nonunique multipliers
    • D.-Z. Du, L. Qi and R.S. Womersley, Eds., World Scientific: Singapore
    • A.B. Levy and R.T. Rockafellar, "Sensitivity of solutions in nonlinear programs with nonunique multipliers," in Recent Advances in Nonsmooth Optimization (D.-Z. Du, L. Qi and R.S. Womersley, Eds.), World Scientific: Singapore, pp. 215-223, 1995.
    • (1995) Recent Advances in Nonsmooth Optimization , pp. 215-223
    • Levy, A.B.1    Rockafellar, R.T.2
  • 28
    • 0030174157 scopus 로고    scopus 로고
    • Variational conditions and the proto-differentiation of partial subgradient mappings
    • A.B. Levy and R.T. Rockafellar, "Variational conditions and the proto-differentiation of partial subgradient mappings," Nonlin. Analysis: Theory, Meth. Appl., vol. 26, pp. 1951-1964, 1996.
    • (1996) Nonlin. Analysis: Theory, Meth. Appl. , vol.26 , pp. 1951-1964
    • Levy, A.B.1    Rockafellar, R.T.2
  • 29
    • 49949133603 scopus 로고
    • The Fritz John necessary optimality conditions in the presence of equality and inequality constraints
    • O.L. Mangasarian and S. Fromovitz, "The Fritz John necessary optimality conditions in the presence of equality and inequality constraints," J. Math. Analysis Appl., vol. 17, pp. 37-47, 1967.
    • (1967) J. Math. Analysis Appl. , vol.17 , pp. 37-47
    • Mangasarian, O.L.1    Fromovitz, S.2
  • 30
    • 84966250815 scopus 로고
    • Complete characterization of openess, metric regularity and Lipschitzian properties of multifunctions
    • B.S. Mordukhovich, "Complete characterization of openess, metric regularity and Lipschitzian properties of multifunctions," Trans. Amer. Math. Soc., vol. 340, pp. 1-35, 1990.
    • (1990) Trans. Amer. Math. Soc. , vol.340 , pp. 1-35
    • Mordukhovich, B.S.1
  • 31
    • 0008693433 scopus 로고
    • Necessary and sufficient conditions for solution stability of parametric nonsmooth equations
    • D.-Z. Du, L. Qi and R.S. Womersley, World Scientific: Singapore
    • J.-S. Pang, "Necessary and sufficient conditions for solution stability of parametric nonsmooth equations," in Recent Advances in Nonsmooth Optimization (D.-Z. Du, L. Qi and R.S. Womersley), World Scientific: Singapore, pp. 261-288, 1995.
    • (1995) Recent Advances in Nonsmooth Optimization , pp. 261-288
    • Pang, J.-S.1
  • 32
    • 0030134439 scopus 로고    scopus 로고
    • Piecewise smoothness, local invertibility, and parametric analysis of normal maps
    • J.-S. Pang and D. Ralph, "Piecewise smoothness, local invertibility, and parametric analysis of normal maps," Math. Oper. Res., vol. 21, pp. 401-426, 1996.
    • (1996) Math. Oper. Res. , vol.21 , pp. 401-426
    • Pang, J.-S.1    Ralph, D.2
  • 34
    • 0029195483 scopus 로고
    • Directional derivatives of the solution of a parametric nonlinear program
    • D. Ralph and S. Dempe, "Directional derivatives of the solution of a parametric nonlinear program," Math. Programming, vol. 70, pp. 159-172, 1995.
    • (1995) Math. Programming , vol.70 , pp. 159-172
    • Ralph, D.1    Dempe, S.2
  • 35
    • 0000444806 scopus 로고    scopus 로고
    • Sensitivity analysis of composite piecewise smooth equations
    • D. Ralph and S. Scholtes, "Sensitivity analysis of composite piecewise smooth equations," Math. Programming B, vol. 76, pp. 593-612, 1997.
    • (1997) Math. Programming B , vol.76 , pp. 593-612
    • Ralph, D.1    Scholtes, S.2
  • 36
    • 0018977011 scopus 로고
    • Strongly regular generalized equations
    • S.M. Robinson, "Strongly regular generalized equations," Math. Oper. Res., vol. 5, pp. 43-62, 1980.
    • (1980) Math. Oper. Res. , vol.5 , pp. 43-62
    • Robinson, S.M.1
  • 37
    • 0001052352 scopus 로고
    • Some continuity properties of polyhedral multifunctions
    • S.M. Robinson, "Some continuity properties of polyhedral multifunctions," Math. Programming Study, vol. 14, pp. 206-214, 1981.
    • (1981) Math. Programming Study , vol.14 , pp. 206-214
    • Robinson, S.M.1
  • 38
    • 0023315165 scopus 로고
    • Local epi-continuity and local optimization
    • S. M. Robinson, "Local epi-continuity and local optimization," Math. Programming, vol. 37, pp. 208-223, 1987.
    • (1987) Math. Programming , vol.37 , pp. 208-223
    • Robinson, S.M.1
  • 39
    • 0000516813 scopus 로고
    • An implicit function theorem for a class of nonsmooth functions
    • S.M. Robinson, "An implicit function theorem for a class of nonsmooth functions," Math. Oper. Res., vol. 16, pp. 292-309, 1991.
    • (1991) Math. Oper. Res. , vol.16 , pp. 292-309
    • Robinson, S.M.1
  • 40
    • 0002954653 scopus 로고
    • Subdifferentials of compactly Lipschitz vector-valued functions
    • L. Thibault, "Subdifferentials of compactly Lipschitz vector-valued functions," Ann. Mat. Pura Appl., vol. 4, pp. 157-192, 1980.
    • (1980) Ann. Mat. Pura Appl. , vol.4 , pp. 157-192
    • Thibault, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.