메뉴 건너뛰기




Volumn 11, Issue 4, 2001, Pages 1119-1144

A nonlinear Lagrangian approach to constrained optimization problems

Author keywords

Augmented Lagrangian; Necessary optimality condition; Nonlinear Lagrangian; Optimal path; Smooth approximate variational principle; Zero duality gap

Indexed keywords


EID: 0035621414     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623400371806     Document Type: Article
Times cited : (74)

References (23)
  • 1
    • 0018523346 scopus 로고
    • Penalty methods for computing points that satisfy second order necessary conditions
    • A. AUSLENDER, Penalty methods for computing points that satisfy second order necessary conditions, Math. Programming, 17 (1979), pp. 229-238.
    • (1979) Math. Programming , vol.17 , pp. 229-238
    • Auslender, A.1
  • 2
    • 0031072276 scopus 로고    scopus 로고
    • Asymptotic analysis for penalty and barrier methods in convex and linear programming
    • A. AUSLENDER, R. COMINETTI, AND M. HADDOU, Asymptotic analysis for penalty and barrier methods in convex and linear programming, Math. Oper. Res., 22 (1997), pp. 43-62.
    • (1997) Math. Oper. Res. , vol.22 , pp. 43-62
    • Auslender, A.1    Cominetti, R.2    Haddou, M.3
  • 3
    • 0000741430 scopus 로고
    • An extension of duality-stability relations to nonconvex optimization problems
    • E. J. BALDER, An extension of duality-stability relations to nonconvex optimization problems, SIAM J. Control Optim., 15 (1977), pp. 329-343.
    • (1977) SIAM J. Control Optim. , vol.15 , pp. 329-343
    • Balder, E.J.1
  • 4
    • 0020176847 scopus 로고
    • Necessary and sufficient optimally conditions for a class of nonsmooth minimization problems
    • A. BEN-TAL AND J. ZOWE, Necessary and sufficient optimally conditions for a class of nonsmooth minimization problems, Math. Programming, 24 (1982), pp. 70-91.
    • (1982) Math. Programming , vol.24 , pp. 70-91
    • Ben-Tal, A.1    Zowe, J.2
  • 6
    • 84966213239 scopus 로고
    • A smooth variational principle with applications to subdifferentiability and differentiability
    • J. M. BORWEIN AND D. PREISS, A smooth variational principle with applications to subdifferentiability and differentiability, Trans. Amer. Math. Soc., 303 (1987), pp. 517-527.
    • (1987) Trans. Amer. Math. Soc. , vol.303 , pp. 517-527
    • Borwein, J.M.1    Preiss, D.2
  • 10
    • 0035534033 scopus 로고    scopus 로고
    • A nonlinear Lagrangian theory for nonconvex optimization
    • C. J. GOH AND X. Q. YANG, A nonlinear Lagrangian theory for nonconvex optimization, J. Optim. Theory Appl., 109 (2001), pp. 99-121.
    • (2001) J. Optim. Theory Appl. , vol.109 , pp. 99-121
    • Goh, C.J.1    Yang, X.Q.2
  • 13
    • 0018441518 scopus 로고
    • Necessary and sufficient conditions for a local minimum. III: Second-order conditions and augmented duality
    • A. D. IOFFE, Necessary and sufficient conditions for a local minimum. III: Second-order conditions and augmented duality, SIAM J. Control Optim., 17 (1979), pp. 266-288.
    • (1979) SIAM J. Control Optim. , vol.17 , pp. 266-288
    • Ioffe, A.D.1
  • 14
    • 21844506739 scopus 로고
    • Zero duality gap for a class of nonconvex optimization problems
    • D. LI, Zero duality gap for a class of nonconvex optimization problems, J. Optim. Theory Appl., 85 (1995), pp. 309-324.
    • (1995) J. Optim. Theory Appl. , vol.85 , pp. 309-324
    • Li, D.1
  • 15
    • 0020167192 scopus 로고
    • Necessary conditions for ∈-optimality
    • P. LORIDAN, Necessary conditions for ∈-optimality, Math. Programming Stud., 19 (1982), pp. 140-152.
    • (1982) Math. Programming Stud. , vol.19 , pp. 140-152
    • Loridan, P.1
  • 16
    • 0003350183 scopus 로고
    • Conjugate Duality and Optimization
    • Philadelphia, PA
    • R. T. ROCKAFELLAR, Conjugate Duality and Optimization, SIAM, Philadelphia, PA, 1974.
    • (1974) SIAM
    • Rockafellar, R.T.1
  • 18
    • 0000606438 scopus 로고    scopus 로고
    • Modified Lagrangian and penalty functions in continuous optimization
    • A. M. RUBINOV, B. M. GLOVER, AND X. Q. YANG, Modified Lagrangian and penalty functions in continuous optimization, Optimization, 46 (1999), pp. 327-351.
    • (1999) Optimization , vol.46 , pp. 327-351
    • Rubinov, A.M.1    Glover, B.M.2    Yang, X.Q.3
  • 19
    • 0033261453 scopus 로고    scopus 로고
    • Decreasing functions with applications to penalization
    • A. M. RUBINOV, B. M. GLOVER, AND X. Q. YANG, Decreasing functions with applications to penalization, SIAM J. Optim., 10 (1999), pp. 289-313.
    • (1999) SIAM J. Optim. , vol.10 , pp. 289-313
    • Rubinov, A.M.1    Glover, B.M.2    Yang, X.Q.3
  • 20
    • 0010932634 scopus 로고
    • Black-box complexity of local minimization
    • S. A. VAVASIS, Black-box complexity of local minimization, SIAM J. Optim., 3 (1993), pp. 60-79.
    • (1993) SIAM J. Optim. , vol.3 , pp. 60-79
    • Vavasis, S.A.1
  • 21
    • 84963198191 scopus 로고
    • 1,1 optimization with applications
    • 1,1 optimization with applications, Numer. Funct. Anal. Optim., 14 (1993), pp. 621-632.
    • (1993) Numer. Funct. Anal. Optim. , vol.14 , pp. 621-632
    • Yang, X.Q.1
  • 22
    • 0013110149 scopus 로고
    • 1,1 optimization problem
    • 1,1 optimization problem, J. Math. Anal. Appl., 87 (1994), pp. 118-133.
    • (1994) J. Math. Anal. Appl. , vol.87 , pp. 118-133
    • Yang, X.Q.1
  • 23
    • 0000812673 scopus 로고    scopus 로고
    • Second-order global optimality conditions for convex composite optimization
    • X. Q. YANG, Second-order global optimality conditions for convex composite optimization, Math. Programming, 81 (1998), pp. 327-347.
    • (1998) Math. Programming , vol.81 , pp. 327-347
    • Yang, X.Q.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.