메뉴 건너뛰기




Volumn 12, Issue 4, 2002, Pages 1075-1089

A globally convergent augmented Lagrangian pattern search algorithm for optimization with general constraints and simple bounds

Author keywords

Augmented Lagrangian; Constrained optimization; Direct search; Nonlinear programming; Pattern search

Indexed keywords


EID: 0036436111     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623498339727     Document Type: Article
Times cited : (262)

References (28)
  • 2
    • 0002606725 scopus 로고
    • A new method of constrained optimization and a comparison with other methods
    • M.J. Box, A new method of constrained optimization and a comparison with other methods, The Computer Journal, 8 (1965), pp. 42-52.
    • (1965) The Computer Journal , vol.8 , pp. 42-52
    • Box, M.J.1
  • 3
    • 0000533741 scopus 로고
    • The created response surface technique for optimizing nonlinear restrained systems
    • C.W. Carroll, The created response surface technique for optimizing nonlinear restrained systems, Oper. Res., 9 (1961), pp. 169-185.
    • (1961) Oper. Res. , vol.9 , pp. 169-185
    • Carroll, C.W.1
  • 4
    • 0026136104 scopus 로고
    • A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds
    • A.R. Conn, N.I.M. Gould, and P.L. Toint, A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds, SIAM J. Numer. Anal., 28 (1991), pp. 545-572.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 545-572
    • Conn, A.R.1    Gould, N.I.M.2    Toint, P.L.3
  • 5
    • 0003141840 scopus 로고
    • LANCELOT: A fortran package for large-scale nonlinear optimization (Release A)
    • Springer-Verlag, New York
    • A.R. Conn, N.I.M. Gould, and P.L. Toint, LANCELOT: A Fortran Package for Large-Scale Nonlinear Optimization (Release A), Springer Ser. Comput. Math. 17, Springer-Verlag, New York, 1992.
    • (1992) Springer Ser. Comput. Math. , vol.17
    • Conn, A.R.1    Gould, N.I.M.2    Toint, P.L.3
  • 6
    • 0011571413 scopus 로고
    • Review of constrained optimization
    • R. Fletcher, ed., Academic Press, New York
    • D. Davies and W.H. Syvann, Review of constrained optimization, in Optimization, R. Fletcher, ed., Academic Press, New York, 1969, pp. 187-202.
    • (1969) Optimization , pp. 187-202
    • Davies, D.1    Syvann, W.H.2
  • 7
    • 0015573121 scopus 로고
    • ACSIM-An accelerated constrained simplex technique
    • L.C.W. Dixon, ACSIM-An accelerated constrained simplex technique, Computer Aided Design, 5 (1973), pp. 22-32.
    • (1973) Computer Aided Design , vol.5 , pp. 22-32
    • Dixon, L.C.W.1
  • 8
    • 0012126939 scopus 로고
    • Nonlinear programming: Sequential unconstrained minimization techniques
    • SIAM, Philadelphia
    • A.V. Fiacco and G.P. Mccormick, Nonlinear Programming: Sequential Unconstrained Minimization Techniques, Classics Appl. Math. 4, SIAM, Philadelphia, 1990.
    • (1990) Classics Appl. Math. , vol.4
    • Fiacco, A.V.1    McCormick, G.P.2
  • 9
    • 0011691468 scopus 로고
    • Sequential search: A method for solving constrained optimization problems
    • H. Glass and L. Cooper, Sequential search: A method for solving constrained optimization problems, J. Assoc. Comput. Machinery, 12 (1965), pp. 71-82.
    • (1965) J. Assoc. Comput. Machinery , vol.12 , pp. 71-82
    • Glass, H.1    Cooper, L.2
  • 10
    • 0011564325 scopus 로고
    • On the simulation and control of some friction constrained motions
    • R. Glowinski and A.J. Kearsley, On the simulation and control of some friction constrained motions, SIAM J. Optim., 5 (1995), pp. 681-694.
    • (1995) SIAM J. Optim. , vol.5 , pp. 681-694
    • Glowinski, R.1    Kearsley, A.J.2
  • 12
    • 84938447945 scopus 로고
    • Direct search solution of numerical and statistical problems
    • R. Hooke and T.A. Jeeves, Direct search solution of numerical and statistical problems, J. Assoc. Comput. Machinery, 8 (1961), pp. 212-229.
    • (1961) J. Assoc. Comput. Machinery , vol.8 , pp. 212-229
    • Hooke, R.1    Jeeves, T.A.2
  • 13
    • 0004079984 scopus 로고    scopus 로고
    • Ph.D. thesis, Department of Computational and Applied Mathematics, Rice University, Houston, TX, available as Tech. report 96-11, Department of Computational and Applied Mathematics, Rice University, Houston, TX
    • A.J. Kearsley, The Use of Optimization Techniques in the Solution of Partial Differential Equations from Science and Engineering, Ph.D. thesis, Department of Computational and Applied Mathematics, Rice University, Houston, TX, 1996; available as Tech. report 96-11, Department of Computational and Applied Mathematics, Rice University, Houston, TX.
    • (1996) The Use of Optimization Techniques in the Solution of Partial Differential Equations from Science and Engineering
    • Kearsley, A.J.1
  • 15
    • 0001053846 scopus 로고
    • Nonlinear programming with the aid of a multiple-gradient summation technique
    • W.R. Klingman and D.M. Himmelblau, Nonlinear programming with the aid of a multiple-gradient summation technique, J. Assoc. Comput. Machinery, 11 (1964), pp. 400-415.
    • (1964) J. Assoc. Comput. Machinery , vol.11 , pp. 400-415
    • Klingman, W.R.1    Himmelblau, D.M.2
  • 16
    • 0003686336 scopus 로고    scopus 로고
    • Tach. report 96-71, Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, Hampton, VA
    • R.M. Lewis and V. Torczon, Rank ordering and positive bases in pattern search algorithms, Tach. report 96-71, Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, Hampton, VA, 1996.
    • (1996) Rank ordering and positive bases in pattern search algorithms
    • Lewis, R.M.1    Torczon, V.2
  • 17
    • 0033412824 scopus 로고    scopus 로고
    • Pattern search algorithms for bound constrained minimization
    • R.M. Lewis and V. Torczon, Pattern search algorithms for bound constrained minimization, SIAM J. Optim., 9 (1999), pp. 1082-1099.
    • (1999) SIAM J. Optim. , vol.9 , pp. 1082-1099
    • Lewis, R.M.1    Torczon, V.2
  • 18
    • 0034412352 scopus 로고    scopus 로고
    • Pattern search methods for linearly constrained minimization
    • R.M. Lewis and V. Torczon, Pattern search methods for linearly constrained minimization, SIAM J. Optim., 10 (2000), pp. 917-941.
    • (2000) SIAM J. Optim. , vol.10 , pp. 917-941
    • Lewis, R.M.1    Torczon, V.2
  • 20
    • 0016538991 scopus 로고
    • A superlinearly convergent algorithm for minimization without evaluating derivatives
    • R. Mifflin, A superlinearly convergent algorithm for minimization without evaluating derivatives, Math. Programming, 9 (1975), pp. 100-117.
    • (1975) Math. Programming , vol.9 , pp. 100-117
    • Mifflin, R.1
  • 21
    • 0000238336 scopus 로고
    • A simplex method for function minimization
    • J.A. Nelder and R. Mead, A simplex method for function minimization, The Computer Journal, 7 (1965), pp. 308-313.
    • (1965) The Computer Journal , vol.7 , pp. 308-313
    • Nelder, J.A.1    Mead, R.2
  • 22
    • 0001581971 scopus 로고
    • Constrained nonlinear optimization by heuristic programming
    • D. Paviani and D.M. Himmelblau, Constrained nonlinear optimization by heuristic programming, Oper. Res., 17 (1969), pp. 872-882.
    • (1969) Oper. Res. , vol.17 , pp. 872-882
    • Paviani, D.1    Himmelblau, D.M.2
  • 23
    • 0015727623 scopus 로고
    • A dual approach to solving nonlinear programming problems by unconstrained optimization
    • R.T. Rockafellar, A dual approach to solving nonlinear programming problems by unconstrained optimization, Math. Programming, 5 (1973), pp. 354-373.
    • (1973) Math. Programming , vol.5 , pp. 354-373
    • Rockafellar, R.T.1
  • 24
    • 0001723141 scopus 로고
    • An automatic method for finding the greatest or least value of a function
    • H.H. Rosenbrock, An automatic method for finding the greatest or least value of a function, The Computer Journal, 3 (1960), pp. 175-184.
    • (1960) The Computer Journal , vol.3 , pp. 175-184
    • Rosenbrock, H.H.1
  • 25
    • 0003320261 scopus 로고
    • Nonlinear least squares fitting using a modified simplex minimization method
    • R. Fletcher, ed., Academic Press, New York
    • W. Spendley, Nonlinear least squares fitting using a modified simplex minimization method, in Optimization, R. Fletcher, ed., Academic Press, New York, 1969, pp. 259-270.
    • (1969) Optimization , pp. 259-270
    • Spendley, W.1
  • 26
    • 84946640734 scopus 로고
    • Sequential application of simplex designs in optimisation and evolutionary operation
    • W. Spendley, G.R. Hext, and F.R. Himsworth, Sequential application of simplex designs in optimisation and evolutionary operation, Technometrics, 4 (1962), pp. 441-461.
    • (1962) Technometrics , vol.4 , pp. 441-461
    • Spendley, W.1    Hext, G.R.2    Himsworth, F.R.3
  • 27
    • 0000728589 scopus 로고
    • Diagonalized multiplier methods and quasi-Newton methods for constrained optimization
    • R.A. Tapia, Diagonalized multiplier methods and quasi-Newton methods for constrained optimization, J. Optim. Theory Appl., 22 (1977), pp. 135-194.
    • (1977) J. Optim. Theory Appl. , vol.22 , pp. 135-194
    • Tapia, R.A.1
  • 28
    • 0031540855 scopus 로고    scopus 로고
    • On the convergence of pattern search algorithms
    • V. Torczon, On the convergence of pattern search algorithms, SIAM J. Optim., 7 (1997), pp. 1-25.
    • (1997) SIAM J. Optim. , vol.7 , pp. 1-25
    • Torczon, V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.