메뉴 건너뛰기




Volumn 38, Issue 1, 1999, Pages 124-137

Lipschitz-type stability in nonsmooth convex programs

Author keywords

[No Author keywords available]

Indexed keywords

CONSTRAINT THEORY; MATRIX ALGEBRA; SENSITIVITY ANALYSIS; SYSTEM STABILITY;

EID: 0342757511     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012996298990     Document Type: Article
Times cited : (6)

References (20)
  • 1
    • 0021375867 scopus 로고
    • Lipschitz behavior of the solution to convex optimization problems
    • J.P. AUBIN, Lipschitz behavior of the solution to convex optimization problems, Math. Oper. Res., 9 (1984), pp. 87-111.
    • (1984) Math. Oper. Res. , vol.9 , pp. 87-111
    • Aubin, J.P.1
  • 2
    • 0001451306 scopus 로고
    • First and second order sensitivity analysis of linear programs under directional constraints qualification condition
    • A. AUSLENDER AND R. COMINETTI, First and second order sensitivity analysis of linear programs under directional constraints qualification condition, Optimization, 21 (1990), pp. 351-363.
    • (1990) Optimization , vol.21 , pp. 351-363
    • Auslender, A.1    Cominetti, R.2
  • 3
    • 0030191876 scopus 로고    scopus 로고
    • Perturbed optimization in Banach spaces I: A general theory based on a weak directionnal constraints qualification
    • J.F. BONNANS AND R. COMINETTI, Perturbed optimization in Banach spaces I: A general theory based on a weak directionnal constraints qualification, SIAM J. Control Optim., 34 (1996), pp. 1151-1171.
    • (1996) SIAM J. Control Optim. , vol.34 , pp. 1151-1171
    • Bonnans, J.F.1    Cominetti, R.2
  • 4
    • 0002622005 scopus 로고
    • Quadratic growth and stability in convex programming problems with multiple solutions
    • J.F. BONNANS AND A.D. IOFFE, Quadratic growth and stability in convex programming problems with multiple solutions, J. Convex Anal., 2 (1995), pp. 41-57.
    • (1995) J. Convex Anal. , vol.2 , pp. 41-57
    • Bonnans, J.F.1    Ioffe, A.D.2
  • 5
    • 0000948820 scopus 로고
    • Implicit functions, Lipschitz maps and stability in optimization
    • A.L. DONTCHEV AND W.W. HAGER, Implicit functions, Lipschitz maps and stability in optimization, Math. Oper. Res., 19 (1994), pp. 753-768.
    • (1994) Math. Oper. Res. , vol.19 , pp. 753-768
    • Dontchev, A.L.1    Hager, W.W.2
  • 7
    • 0001094705 scopus 로고
    • Directional behavior of the optimal solutions in nonlinear mathematical programming
    • J. GAUVIN AND R. JANIN, Directional behavior of the optimal solutions in nonlinear mathematical programming, Math. Oper. Res., 13 (1988), pp. 629-649.
    • (1988) Math. Oper. Res. , vol.13 , pp. 629-649
    • Gauvin, J.1    Janin, R.2
  • 8
    • 0009041189 scopus 로고
    • Directional Lipschitzian optimal solutions and directional derivative for the optimal value function in nonlinear mathematical programming
    • J. GAUVIN AND R. JANIN, Directional Lipschitzian optimal solutions and directional derivative for the optimal value function in nonlinear mathematical programming, Ann. Inst. H. Poincaré Anal. Non Linéaire, 6 (1989), Supp., pp. 305-324.
    • (1989) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.6 , Issue.SUPPL. , pp. 305-324
    • Gauvin, J.1    Janin, R.2
  • 10
    • 0003207518 scopus 로고
    • Lipschitz dependence of the optimal solution to elementary convex programs
    • Font-Romeu, Odeillo, France, M. Sofonea, ed., Presses Universitaires de Perpignan, Perpignan, France
    • R. JANIN AND J. GAUVIN, Lipschitz dependence of the optimal solution to elementary convex programs, in Proceedings of the 2nd Catalan Days on Applied Mathematics, Font-Romeu, Odeillo, France, M. Sofonea, ed., Presses Universitaires de Perpignan, Perpignan, France, 1995, pp. 149-161.
    • (1995) Proceedings of the 2nd Catalan Days on Applied Mathematics , pp. 149-161
    • Janin, R.1    Gauvin, J.2
  • 11
    • 0342889689 scopus 로고
    • Linear stability of generalized equations parts I and II
    • L. JIMING, Linear stability of generalized equations parts I and II, Math. Oper. Res., 19 (1994), pp. 706-742.
    • (1994) Math. Oper. Res. , vol.19 , pp. 706-742
    • Jiming, L.1
  • 12
    • 0021446932 scopus 로고
    • Solution point differentiability without strict complementarity in nonlinear programming
    • K. JITTORNTRUM, Solution point differentiability without strict complementarity in nonlinear programming, Math. Programming, 21 (1984), pp. 127-138.
    • (1984) Math. Programming , vol.21 , pp. 127-138
    • Jittorntrum, K.1
  • 14
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton, NJ
    • R.T. ROCKAFELLAR, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 15
    • 0016993914 scopus 로고
    • Stability theory for systems of inequalities, part II: Differentiable nonlinear systems
    • S.M. ROBINSON, Stability theory for systems of inequalities, part II: Differentiable nonlinear systems, SIAM J. Numer. Anal., 13 (1976), pp. 497-513.
    • (1976) SIAM J. Numer. Anal. , vol.13 , pp. 497-513
    • Robinson, S.M.1
  • 16
    • 0018977011 scopus 로고
    • Strongly regular generalized equations
    • S.M. ROBINSON, Strongly regular generalized equations, Math. Oper. Res., 5 (1980), pp. 43-62.
    • (1980) Math. Oper. Res. , vol.5 , pp. 43-62
    • Robinson, S.M.1
  • 17
    • 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., 16 (1991), pp. 292-309.
    • (1991) Math. Oper. Res. , vol.16 , pp. 292-309
    • Robinson, S.M.1
  • 18
    • 0007282005 scopus 로고
    • On Lipschitzian stability of optimal solutions of parametrized semi-infinite programs
    • A. SHAPIRO, On Lipschitzian stability of optimal solutions of parametrized semi-infinite programs, Math. Oper. Res., 19 (1994), pp. 743-752.
    • (1994) Math. Oper. Res. , vol.19 , pp. 743-752
    • Shapiro, A.1
  • 19
    • 0022361755 scopus 로고
    • Second order sensitivity analysis and asymptotic theory of parametrized, nonlinear programs
    • A. SHAPIRO, Second order sensitivity analysis and asymptotic theory of parametrized, nonlinear programs, Math. Programming, 33 (1985), pp. 280-299.
    • (1985) Math. Programming , vol.33 , pp. 280-299
    • Shapiro, A.1
  • 20
    • 0024001357 scopus 로고
    • Sensitivity analysis of nonlinear programs and differentiability properties of metric projections
    • A. SHAPIRO, Sensitivity analysis of nonlinear programs and differentiability properties of metric projections, SIAM J. Control Optim., 26 (1988), pp. 628-645.
    • (1988) SIAM J. Control Optim. , vol.26 , pp. 628-645
    • Shapiro, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.