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Volumn 86, Issue 3, 1999, Pages 615-635

Superlinear and quadratic convergence of affine-scaling interior-point Newton methods for problems with simple bounds without strict complementarity assumption

Author keywords

Affine scaling; Bound constraints; Degeneracy; Interior point algorithms; Nonlinear programming; Optimality conditions; Superlinear convergence

Indexed keywords


EID: 0000860416     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/s101070050107     Document Type: Article
Times cited : (66)

References (28)
  • 1
    • 0000377218 scopus 로고
    • Projected Newton methods for optimization problems with simple constraints
    • Bertsekas, D.P. (1982): Projected Newton methods for optimization problems with simple constraints. SIAM J. Control Optim. 20, 221-246
    • (1982) SIAM J. Control Optim. , vol.20 , pp. 221-246
    • Bertsekas, D.P.1
  • 2
    • 0031285895 scopus 로고    scopus 로고
    • A trust region interior point algorithm for linearly constrained optimization
    • Bonnans, J.F., Pola, C. (1997): A trust region interior point algorithm for linearly constrained optimization. SIAM J. Optim. 7, 717-731
    • (1997) SIAM J. Optim. , vol.7 , pp. 717-731
    • Bonnans, J.F.1    Pola, C.2
  • 3
    • 34249771074 scopus 로고
    • On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds
    • Coleman, T.F., Li, Y. (1994): On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds. Math. Program. 67, 189-224
    • (1994) Math. Program. , vol.67 , pp. 189-224
    • Coleman, T.F.1    Li, Y.2
  • 4
    • 0030303844 scopus 로고    scopus 로고
    • An interior trust region approach for nonlinear minimization subject to bounds
    • Coleman, T.F., Li, Y. (1996): An interior trust region approach for nonlinear minimization subject to bounds. SIAM J. Optim. 6, 418-445.
    • (1996) SIAM J. Optim. , vol.6 , pp. 418-445
    • Coleman, T.F.1    Li, Y.2
  • 6
    • 0002467356 scopus 로고
    • Global convergence of a class of trust region algorithms for optimization with simple bounds
    • See [7]
    • Conn, A.R., Gould, N.I.M., Toint, Ph.L. (1988): Global convergence of a class of trust region algorithms for optimization with simple bounds. SIAM J. Numer. Anal. 25, 433-460. See [7]
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 433-460
    • Conn, A.R.1    Gould, N.I.M.2    Toint, Ph.L.3
  • 7
    • 0001623391 scopus 로고
    • Correction to the paper on global convergence of a class of trust region algorithms for optimization with simple bounds
    • Conn, A.R., Gould, N.I.M., Toint, Ph.L. (1989): Correction to the paper on global convergence of a class of trust region algorithms for optimization with simple bounds. SIAM J. Numer. Anal. 26, 764-767
    • (1989) SIAM J. Numer. Anal. , vol.26 , pp. 764-767
    • Conn, A.R.1    Gould, N.I.M.2    Toint, Ph.L.3
  • 8
    • 0032165036 scopus 로고    scopus 로고
    • Trust-region interior-point algorithms fora class of nonlinear programming problems
    • Dennis, J.E., Heinkenschloss, M., Vicente, L.N. (1998): Trust-region interior-point algorithms fora class of nonlinear programming problems. SIAM J. Control Optim. 36, 1750-1794
    • (1998) SIAM J. Control Optim. , vol.36 , pp. 1750-1794
    • Dennis, J.E.1    Heinkenschloss, M.2    Vicente, L.N.3
  • 9
    • 0012448399 scopus 로고    scopus 로고
    • Trust-region interior-point algorithms for minimization methods with simple bounds
    • Fischer, H., Riedmüller, B., Schäffler, S., eds., Festschrift for Klaus Ritter, Physica-Verlag, Heidelberg
    • Dennis, J.E., Vicente, L.N. (1996): Trust-region interior-point algorithms for minimization methods with simple bounds. In: Fischer, H., Riedmüller, B., Schäffler, S., eds., Applied Mathematics and Parallel Computing, Festschrift for Klaus Ritter, pp. 97-107. Physica-Verlag, Heidelberg
    • (1996) Applied Mathematics and Parallel Computing , pp. 97-107
    • Dennis, J.E.1    Vicente, L.N.2
  • 10
    • 0030541525 scopus 로고    scopus 로고
    • On the formulation and theory of the primal-dual Newton interior-point method for nonlinear programming
    • El-Bakry, A.S., Tapia, R.A., Tsuchiya, T., Zhang, Y. (1996): On the formulation and theory of the primal-dual Newton interior-point method for nonlinear programming. J. Optim. Theory Appl. 89, 507-541
    • (1996) J. Optim. Theory Appl. , vol.89 , pp. 507-541
    • El-Bakry, A.S.1    Tapia, R.A.2    Tsuchiya, T.3    Zhang, Y.4
  • 11
    • 0030242534 scopus 로고    scopus 로고
    • On the convergence rate of Newton interior-point methods in the absence of strict complementarity
    • El-Bakry, A.S., Tapia, R.A., Zhang, Y. (1996): On the convergence rate of Newton interior-point methods in the absence of strict complementarity. Comput. Optim. Appl. 6, 157-167
    • (1996) Comput. Optim. Appl. , vol.6 , pp. 157-167
    • El-Bakry, A.S.1    Tapia, R.A.2    Zhang, Y.3
  • 12
    • 0001151466 scopus 로고    scopus 로고
    • A nonsmooth inexact Newton method for the solution of large-scale nonlinear complementarity problems
    • Facchinei, F., Kanzow, C. (1997): A nonsmooth inexact Newton method for the solution of large-scale nonlinear complementarity problems. Math. Program. 76, 493-512
    • (1997) Math. Program. , vol.76 , pp. 493-512
    • Facchinei, F.1    Kanzow, C.2
  • 13
    • 0003268454 scopus 로고
    • Introduction to Sensitivity and Stability Analysis in Nonlinear Programming
    • Academic Press, New York
    • Fiacco, A.V. (1983): Introduction to Sensitivity and Stability Analysis in Nonlinear Programming. Mathematics in Science and Engineering, Vol. 165. Academic Press, New York
    • (1983) Mathematics in Science and Engineering , vol.165
    • Fiacco, A.V.1
  • 15
    • 84948263182 scopus 로고
    • A special Newton-type optimization method
    • Fischer, A. (1992): A special Newton-type optimization method. Optimization 24, 269-284
    • (1992) Optimization , vol.24 , pp. 269-284
    • Fischer, A.1
  • 16
    • 0000554369 scopus 로고    scopus 로고
    • Solution of monotone complementarity problems with locally Lipschitzian functions
    • Fischer, A. (1997): Solution of monotone complementarity problems with locally Lipschitzian functions. Math. Program. 76, 513-532
    • (1997) Math. Program. , vol.76 , pp. 513-532
    • Fischer, A.1
  • 17
    • 0031542596 scopus 로고    scopus 로고
    • On the convergence of the Mizuno-Todd-Ye algorithm to the analytic center of the solution set
    • Gonzaga, C.C., Tapia, R.A. (1997): On the convergence of the Mizuno-Todd-Ye algorithm to the analytic center of the solution set. SIAM J. Optim. 7, 47-65
    • (1997) SIAM J. Optim. , vol.7 , pp. 47-65
    • Gonzaga, C.C.1    Tapia, R.A.2
  • 18
    • 0026136905 scopus 로고
    • Convergence of trust region algorithms for optimization with bounds when strict complementarity does not hold
    • Lescrenier, M. (1991): Convergence of trust region algorithms for optimization with bounds when strict complementarity does not hold. SIAM J. Numer. Anal. 28, 476-495
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 476-495
    • Lescrenier, M.1
  • 19
    • 0038111250 scopus 로고    scopus 로고
    • Technical Report ANL/MCS-P724-0898, Mathematics and Computer Sciences Division, Argonne National Laboratories, 9700 South Cass Avenue, Argonne, Ill. 60439
    • Lin, C.-J., Moré, J.J. (1998): Newton's method for large bound-constrained optimization problems. Technical Report ANL/MCS-P724-0898, Mathematics and Computer Sciences Division, Argonne National Laboratories, 9700 South Cass Avenue, Argonne, Ill. 60439
    • (1998) Newton's Method for Large Bound-Constrained Optimization Problems
    • Lin, C.-J.1    Moré, J.J.2
  • 20
    • 0028436629 scopus 로고
    • Local convergence of interior point algorithms for degenerate monotone LCP
    • Monteiro, R.D.C., Wright, S.J. (1994): Local convergence of interior point algorithms for degenerate monotone LCP. Comput. Optim. Appl. 3, 131-155
    • (1994) Comput. Optim. Appl. , vol.3 , pp. 131-155
    • Monteiro, R.D.C.1    Wright, S.J.2
  • 21
    • 0018977011 scopus 로고
    • Strongly regular generalized equations
    • Robinson, S.M. (1980): Strongly regular generalized equations. Math. Oper. Res. 5, 43-62
    • (1980) Math. Oper. Res. , vol.5 , pp. 43-62
    • Robinson, S.M.1
  • 22
    • 0027607278 scopus 로고
    • A convergence proof for an affine-scaling algorithm for convex quadratic programming without nondegeneracy assumptions
    • Sun, J. (1993): A convergence proof for an affine-scaling algorithm for convex quadratic programming without nondegeneracy assumptions. Math. Program. 60, 69-79
    • (1993) Math. Program. , vol.60 , pp. 69-79
    • Sun, J.1
  • 23
    • 85038070178 scopus 로고    scopus 로고
    • Superlinear convergence of affine-scaling interior-point newton methods for infinite-dimensional nonlinear problems with pointwise bounds
    • TR97-05, Department of Computational and Applied Mathematics, Rice University, Houston, Texas. Accepted subject to revisions for publication
    • Ulbrich, M., Ulbrich, S. (1997): Superlinear convergence of affine-scaling interior-point newton methods for infinite-dimensional nonlinear problems with pointwise bounds. TR97-05, Department of Computational and Applied Mathematics, Rice University, Houston, Texas. Accepted subject to revisions for publication in SIAM J. Control Optim.
    • (1997) SIAM J. Control Optim.
    • Ulbrich, M.1    Ulbrich, S.2
  • 24
    • 0032651455 scopus 로고    scopus 로고
    • Global convergence of affine-scaling interior-point Newton methods for infinite-dimensional nonlinear problems with pointwise bounds
    • Ulbrich, M., Ulbrich, S., Heinkenschloss, M. (1999): Global convergence of affine-scaling interior-point Newton methods for infinite-dimensional nonlinear problems with pointwise bounds. SIAM J. Control Optimization 37, 731-764
    • (1999) SIAM J. Control Optimization , vol.37 , pp. 731-764
    • Ulbrich, M.1    Ulbrich, S.2    Heinkenschloss, M.3
  • 25
    • 0031677102 scopus 로고    scopus 로고
    • On interior-point Newton algorithms for discretized optimal control problems with state constraints
    • Vicente, L.N. (1998): On interior-point Newton algorithms for discretized optimal control problems with state constraints. Optim. Methods Softw. 8, 249-275
    • (1998) Optim. Methods Softw. , vol.8 , pp. 249-275
    • Vicente, L.N.1
  • 26
    • 84971922797 scopus 로고
    • Interior point methods for constrained optimization
    • Iserles, A., ed., Cambridge University Press, Cambridge, London, New York
    • Wright, M.H. (1992): Interior point methods for constrained optimization. In: Iserles, A., ed., Acta Numerica 1992, pp. 341-407. Cambridge University Press, Cambridge, London, New York
    • (1992) Acta Numerica 1992 , pp. 341-407
    • Wright, M.H.1
  • 28
    • 0000273506 scopus 로고    scopus 로고
    • Superlinear and quadratic convergence of some primal-dual interior point methods for constrained optimization
    • Yamashita, H., Yabe, H. (1996): Superlinear and quadratic convergence of some primal-dual interior point methods for constrained optimization. Math. Program. 75, 377-397
    • (1996) Math. Program. , vol.75 , pp. 377-397
    • Yamashita, H.1    Yabe, H.2


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