메뉴 건너뛰기




Volumn 10, Issue 2, 1999, Pages 605-625

A truly globally convergent Newton-type method for the monotone nonlinear complementarity problem

Author keywords

Global convergence; Newton method; Nonlinear complementarity problem; Projection method; Proximal point method; Superlinear convergence

Indexed keywords


EID: 0040196039     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/s1052623498337546     Document Type: Article
Times cited : (40)

References (53)
  • 1
    • 0028385352 scopus 로고
    • Local analysis of Newton-type methods for variational inequalities and nonlinear programming
    • J. F. BONNANS, Local analysis of Newton-type methods for variational inequalities and nonlinear programming, Appl. Math. Optim., 29 (1994), pp. 161-186.
    • (1994) Appl. Math. Optim. , vol.29 , pp. 161-186
    • Bonnans, J.F.1
  • 3
    • 0029423693 scopus 로고
    • The PATH solver: A nonmonotone stabilization scheme for mixed complementarity problems
    • S. P. DIRKSE AND M. C. FERRIS, The PATH solver: A nonmonotone stabilization scheme for mixed complementarity problems, Optim. Methods Softw., 5 (1995), pp. 123-156.
    • (1995) Optim. Methods Softw. , vol.5 , pp. 123-156
    • Dirkse, S.P.1    Ferris, M.C.2
  • 4
    • 0002528119 scopus 로고    scopus 로고
    • Inexact Newton methods for semismooth equations with applications to variational inequality problems
    • G. D. Pillo and F. Giannessi, eds., Plenum Press, New York
    • F. FACCHINEI, A. FISCHER, AND C. KANZOW, Inexact Newton methods for semismooth equations with applications to variational inequality problems, in Nonlinear Optimization and Applications, G. D. Pillo and F. Giannessi, eds., Plenum Press, New York, 1996, pp. 125-139.
    • (1996) Nonlinear Optimization and Applications , pp. 125-139
    • Facchinei, F.1    Fischer, A.2    Kanzow, C.3
  • 5
    • 0032657647 scopus 로고    scopus 로고
    • Beyond monotonicity in regularization methods for nonlinear complementarity problems
    • F. FACCHINEI AND C. KANZOW, Beyond monotonicity in regularization methods for nonlinear complementarity problems, SIAM J. Control Optim., 37 (1999), pp. 150-1161.
    • (1999) SIAM J. Control Optim. , vol.37 , pp. 150-1161
    • Facchinei, F.1    Kanzow, C.2
  • 6
    • 0031542397 scopus 로고    scopus 로고
    • A new merit function for nonlinear complementarity problems and a related algorithm
    • F. FACCHINEI AND J. SOARES, A new merit function for nonlinear complementarity problems and a related algorithm, SIAM J. Optim., 7 (1997), pp. 225-247.
    • (1997) SIAM J. Optim. , vol.7 , pp. 225-247
    • Facchinei, F.1    Soares, J.2
  • 8
    • 0000203179 scopus 로고    scopus 로고
    • Feasible descent algorithms for mixed complementarity problems
    • M. C. FERRIS, C. KANZOW, AND T. S. MUNSON, Feasible descent algorithms for mixed complementarity problems, Math. Programming, 86 (1999), pp. 475-497.
    • (1999) Math. Programming , vol.86 , pp. 475-497
    • Ferris, M.C.1    Kanzow, C.2    Munson, T.S.3
  • 9
    • 84948263182 scopus 로고
    • A special Newton-type optimization method
    • A. FISCHER, A special Newton-type optimization method, Optimization, 24 (1992), pp. 269-284.
    • (1992) Optimization , vol.24 , pp. 269-284
    • Fischer, A.1
  • 10
    • 0002132714 scopus 로고
    • An NCP function and its use for the solution of complementarity problems
    • D.-Z. Du, L. Qi, and R. Womersley, eds., World Scientific Publishers, Singapore
    • A. FISCHER, An NCP function and its use for the solution of complementarity problems, in Recent Advances in Nonsmooth Optimization, D.-Z. Du, L. Qi, and R. Womersley, eds., World Scientific Publishers, Singapore, 1995, pp. 88-105.
    • (1995) Recent Advances in Nonsmooth Optimization , pp. 88-105
    • Fischer, A.1
  • 11
    • 0026763569 scopus 로고
    • Equivalent differentiate optimization problems and descent methods for asymmetric variational inequality problems
    • M. FUKUSHIMA, Equivalent differentiate optimization problems and descent methods for asymmetric variational inequality problems, Math. Programming, 53 (1992), pp. 99-110.
    • (1992) Math. Programming , vol.53 , pp. 99-110
    • Fukushima, M.1
  • 12
    • 0002358032 scopus 로고    scopus 로고
    • Merit functions for variational inequality and complementarity problems
    • G. D. Pillo and F. Giannessi, eds., Plenum Press, New York
    • M. FUKUSHIMA, Merit functions for variational inequality and complementarity problems, in Nonlinear Optimization and Applications, G. D. Pillo and F. Giannessi, eds., Plenum Press, New York, 1996, pp. 155-170.
    • (1996) Nonlinear Optimization and Applications , pp. 155-170
    • Fukushima, M.1
  • 14
    • 0344704362 scopus 로고
    • Finite-dimensional variational inequality problems: A survey of theory, algorithms and applications
    • P. HARKER AND J.-S. PANG, Finite-dimensional variational inequality problems: A survey of theory, algorithms and applications, Math. Programming, 48 (1990), pp. 161-220.
    • (1990) Math. Programming , vol.48 , pp. 161-220
    • Harker, P.1    Pang, J.-S.2
  • 15
    • 0030736633 scopus 로고    scopus 로고
    • A new nonsmooth equations approach to nonlinear complementarity problems
    • H. JIANG AND L. QI, A new nonsmooth equations approach to nonlinear complementarity problems, SIAM J. Control Optim., 35 (1997), pp. 178-193.
    • (1997) SIAM J. Control Optim. , vol.35 , pp. 178-193
    • Jiang, H.1    Qi, L.2
  • 16
    • 0012374684 scopus 로고    scopus 로고
    • Global and local superlinear convergence analysis of Newton-type methods for semismooth equations with smooth least squares
    • M. Fukushima and L. Qi, eds., Kluwer Academic Publishers, Norwell, MA
    • H. JIANG AND D. RALPH, Global and local superlinear convergence analysis of Newton-type methods for semismooth equations with smooth least squares, in Reformulation -Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, M. Fukushima and L. Qi, eds., Kluwer Academic Publishers, Norwell, MA, 1998, pp. 181-210.
    • (1998) Reformulation -nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods , pp. 181-210
    • Jiang, H.1    Ralph, D.2
  • 17
    • 0004219579 scopus 로고
    • Technical Summary Report 1965, Mathematics Research Center, University of Wisconsin, Madison, WI
    • N. JOSEPHY, Newton's Method for Generalized Equations, Technical Summary Report 1965, Mathematics Research Center, University of Wisconsin, Madison, WI, 1979.
    • (1979) Newton's Method for Generalized Equations
    • Josephy, N.1
  • 18
    • 0028712609 scopus 로고
    • Some equation-based methods for the nonlinear complementarity problem
    • C. KANZOW, Some equation-based methods for the nonlinear complementarity problem, Optim. Methods Softw., 3 (1994), pp. 327-340.
    • (1994) Optim. Methods Softw. , vol.3 , pp. 327-340
    • Kanzow, C.1
  • 19
    • 0030540616 scopus 로고    scopus 로고
    • Nonlinear complementarity as unconstrained optimization
    • C. KANZOW, Nonlinear complementarity as unconstrained optimization, J. Optim. Theory Appl., 88 (1996), pp. 139-155.
    • (1996) J. Optim. Theory Appl. , vol.88 , pp. 139-155
    • Kanzow, C.1
  • 20
    • 0002222760 scopus 로고    scopus 로고
    • Theoretical and numerical investigation of the D-gap function for box constrained variational inequalities
    • C. KANZOW AND M. FUKUSHIMA, Theoretical and numerical investigation of the D-gap function for box constrained variational inequalities, Math. Programming, 83 (1998), pp. 55-87.
    • (1998) Math. Programming , vol.83 , pp. 55-87
    • Kanzow, C.1    Fukushima, M.2
  • 21
    • 0043189808 scopus 로고    scopus 로고
    • A semismooth equation approach to the solution of nonlinear complementarity problems
    • T. D. LUCA, F. FACCHINEI, AND C. KANZOW, A semismooth equation approach to the solution of nonlinear complementarity problems, Math. Programming, 75 (1996), pp. 407-439.
    • (1996) Math. Programming , vol.75 , pp. 407-439
    • Luca, T.D.1    Facchinei, F.2    Kanzow, C.3
  • 22
    • 0003128905 scopus 로고    scopus 로고
    • A new class of merit functions for the nonlinear complementarity problem
    • M. C. Ferris and J.-S. Pang, eds., SIAM, Philadelphia, PA
    • Z.-Q. LUO AND P. TSENG, A new class of merit functions for the nonlinear complementarity problem, in Complementarity and Variational Problems: State of the art, M. C. Ferris and J.-S. Pang, eds., SIAM, Philadelphia, PA, 1997, pp. 204-225.
    • (1997) Complementarity and Variational Problems: State of the Art , pp. 204-225
    • Luo, Z.-Q.1    Tseng, P.2
  • 23
    • 34250076671 scopus 로고
    • Nonlinear complementarity as unconstrained and constrained minimization
    • O. L. MANGASARIAN AND M. V. SOLODOV, Nonlinear complementarity as unconstrained and constrained minimization, Math. Programming, 62 (1993), pp. 277-297.
    • (1993) Math. Programming , vol.62 , pp. 277-297
    • Mangasarian, O.L.1    Solodov, M.V.2
  • 24
    • 0032662717 scopus 로고    scopus 로고
    • A linearly convergent derivative-free descent method for strongly monotone complementarity problems
    • O. L. MANGASARIAN AND M. V. SOLODOV, A linearly convergent derivative-free descent method for strongly monotone complementarity problems, Comput. Optim. Appl., 14 (1999), pp. 5-16.
    • (1999) Comput. Optim. Appl. , vol.14 , pp. 5-16
    • Mangasarian, O.L.1    Solodov, M.V.2
  • 25
    • 0023314787 scopus 로고
    • A note on a globally convergent newton method for solving monotone variational inequalities
    • P. MARCOTTE AND J.-P. DUSSAULT, A note on a globally convergent Newton method for solving monotone variational inequalities, Oper. Res. Lett., 6 (1987), pp. 35-42.
    • (1987) Oper. Res. Lett. , vol.6 , pp. 35-42
    • Marcotte, P.1    Dussault, J.-P.2
  • 26
    • 0022792007 scopus 로고
    • Inexact Newton methods for the nonlinear complementarity problem
    • J.-S. PANG, Inexact Newton methods for the nonlinear complementarity problem, Math. Programming, 36 (1986), pp. 54-71.
    • (1986) Math. Programming , vol.36 , pp. 54-71
    • Pang, J.-S.1
  • 27
    • 0001170028 scopus 로고
    • A posteriori error bounds for the linearly-constrained variational inequality problem
    • J.-S. PANG, A posteriori error bounds for the linearly-constrained variational inequality problem, Math. Oper. Res., 12 (1987), pp. 474-484.
    • (1987) Math. Oper. Res. , vol.12 , pp. 474-484
    • Pang, J.-S.1
  • 28
    • 0003000071 scopus 로고
    • Complementarity problems
    • R. Horst and P. Pardalos, eds., Kluwer Academic Publishers, Boston, MA
    • J.-S. PANG, Complementarity problems, in Handbook of Global Optimization, R. Horst and P. Pardalos, eds., Kluwer Academic Publishers, Boston, MA, 1995, pp. 271-338.
    • (1995) Handbook of Global Optimization , pp. 271-338
    • Pang, J.-S.1
  • 29
    • 0000150038 scopus 로고    scopus 로고
    • Error bounds in mathematical programming
    • J.-S. PANG, Error bounds in mathematical programming, Math. Programming, 79 (1997), pp. 299-332.
    • (1997) Math. Programming , vol.79 , pp. 299-332
    • Pang, J.-S.1
  • 30
    • 0020243016 scopus 로고
    • Iterative methods for variational and complementarity problems
    • J.-S. PANG AND D. CHAN, Iterative methods for variational and complementarity problems, Math. Programming, 24 (1982), pp. 284-313.
    • (1982) Math. Programming , vol.24 , pp. 284-313
    • Pang, J.-S.1    Chan, D.2
  • 31
    • 0000860428 scopus 로고    scopus 로고
    • A hybrid newton method for solving the variational inequality problem via the D-gap function
    • J.-M. PENG AND M. FUKUSHIMA, A hybrid Newton method for solving the variational inequality problem via the D-gap function, Math. Programming, 86 (1999), pp. 367-386.
    • (1999) Math. Programming , vol.86 , pp. 367-386
    • Peng, J.-M.1    Fukushima, M.2
  • 32
    • 0032670483 scopus 로고    scopus 로고
    • A hybrid josephy-newton method for solving box constrained variational inequality problem via the D-gap function
    • J.-M. PENG, C. KANZOW, AND M. FUKUSHIMA, A hybrid Josephy-Newton method for solving box constrained variational inequality problem via the D-gap function, Optim. Methods Softw., 10 (1999), pp. 687-710.
    • (1999) Optim. Methods Softw. , vol.10 , pp. 687-710
    • Peng, J.-M.1    Kanzow, C.2    Fukushima, M.3
  • 33
    • 85049776636 scopus 로고
    • Optimization Software, Inc., Publications Division, New York
    • B. T. POLYAK, Introduction to Optimization, Optimization Software, Inc., Publications Division, New York, 1987.
    • (1987) Introduction to Optimization
    • Polyak, B.T.1
  • 34
    • 0001393203 scopus 로고
    • Global convergence of damped Newton's method for nonsmooth equations via the path search
    • D. RALPH, Global convergence of damped Newton's method for nonsmooth equations via the path search, Math. Oper. Res., 19 (1994), pp. 352-389.
    • (1994) Math. Oper. Res. , vol.19 , pp. 352-389
    • Ralph, D.1
  • 35
    • 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
  • 36
    • 0001272077 scopus 로고
    • Normal maps induced by linear transformations
    • S. M. ROBINSON, Normal maps induced by linear transformations, Math. Oper. Res., 17 (1992), pp. 691-714.
    • (1992) Math. Oper. Res. , vol.17 , pp. 691-714
    • Robinson, S.M.1
  • 37
    • 0016985417 scopus 로고
    • Monotone operators and the proximal point algorithm
    • R. T. ROCKAFELLAR, Monotone operators and the proximal point algorithm, SIAM J. Control Optim., 14 (1976), pp. 877-898.
    • (1976) SIAM J. Control Optim. , vol.14 , pp. 877-898
    • Rockafellar, R.T.1
  • 38
    • 15744389126 scopus 로고    scopus 로고
    • A comparison of rates of convergence of two inexact proximal point algorithms
    • G. D. Pillo and F. Giannessi, eds., Kluwer Academic Publishers, Norwell, MA, to appear
    • M. SOLODOV AND B. SVAITER, A comparison of rates of convergence of two inexact proximal point algorithms, in Nonlinear Optimization and Related Topics, G. D. Pillo and F. Giannessi, eds., Kluwer Academic Publishers, Norwell, MA, to appear.
    • Nonlinear Optimization and Related Topics
    • Solodov, M.1    Svaiter, B.2
  • 39
    • 84923748549 scopus 로고    scopus 로고
    • Forcing strong convergence of proximal point iterations in a hubert space
    • to appear
    • M. SOLODOV AND B. SVAITER, Forcing strong convergence of proximal point iterations in a Hubert space, Math. Programming, to appear.
    • Math. Programming
    • Solodov, M.1    Svaiter, B.2
  • 40
    • 0003124748 scopus 로고    scopus 로고
    • A globally convergent inexact newton method for systems of monotone equations
    • M. Fukushima and L. Qi, eds., Kluwer Academic Publishers, Norwell, MA
    • M. SOLODOV AND B. SVAITER, A globally convergent inexact Newton method for systems of monotone equations, in Reformulation - Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, M. Fukushima and L. Qi, eds., Kluwer Academic Publishers, Norwell, MA, 1998, pp. 355-369.
    • (1998) Reformulation - Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods , pp. 355-369
    • Solodov, M.1    Svaiter, B.2
  • 41
    • 0000586985 scopus 로고    scopus 로고
    • A hybrid approximate extragradient - Proximal point algorithm using the enlargement of a maximal monotone operator
    • M. SOLODOV AND B. SVAITER, A hybrid approximate extragradient - proximal point algorithm using the enlargement of a maximal monotone operator, Set-Valued Anal., 7 (1999), pp. 323-345.
    • (1999) Set-Valued Anal. , vol.7 , pp. 323-345
    • Solodov, M.1    Svaiter, B.2
  • 42
    • 84923748548 scopus 로고    scopus 로고
    • Error bounds for proximal point subproblems and associated inexact proximal point algorithms
    • submitted
    • M. SOLODOV AND B. SVAITER, Error bounds for proximal point subproblems and associated inexact proximal point algorithms, Math. Programming, submitted.
    • Math. Programming
    • Solodov, M.1    Svaiter, B.2
  • 43
    • 22844456506 scopus 로고    scopus 로고
    • A hybrid projection - Proximal point algorithm
    • M. SOLODOV AND B. SVAITER, A hybrid projection - proximal point algorithm, J. Convex Anal., 6 (1999), pp. 59-70.
    • (1999) J. Convex Anal. , vol.6 , pp. 59-70
    • Solodov, M.1    Svaiter, B.2
  • 44
    • 0031503709 scopus 로고    scopus 로고
    • Stationary points of bound constrained reformulations of complementarity problems
    • M. V. SOLODOV, Stationary points of bound constrained reformulations of complementarity problems, J. Optim. Theory Appl., 94 (1997), pp. 449-467.
    • (1997) J. Optim. Theory Appl. , vol.94 , pp. 449-467
    • Solodov, M.V.1
  • 46
    • 0000126539 scopus 로고    scopus 로고
    • Some optimization reformulations of the extended linear complementarity problem
    • M. V. SOLODOV, Some optimization reformulations of the extended linear complementarity problem, Comput. Optim. Appl., 12 (1999), pp. 187-200.
    • (1999) Comput. Optim. Appl. , vol.12 , pp. 187-200
    • Solodov, M.V.1
  • 47
    • 0032632635 scopus 로고    scopus 로고
    • A new projection method for variational inequality problems
    • M. V. SOLODOV AND B. F. SVAITER, A new projection method for variational inequality problems, SIAM J. Control Optim., 37 (1999), pp. 765-776.
    • (1999) SIAM J. Control Optim. , vol.37 , pp. 765-776
    • Solodov, M.V.1    Svaiter, B.F.2
  • 48
    • 0032682238 scopus 로고    scopus 로고
    • A regularization Newton method for solving nonlinear complementarity problems
    • D. SUN, A regularization Newton method for solving nonlinear complementarity problems, Appl. Math. Optim., 40 (1999), pp. 315-339.
    • (1999) Appl. Math. Optim. , vol.40 , pp. 315-339
    • Sun, D.1
  • 49
    • 0001321899 scopus 로고    scopus 로고
    • A computable generalized Hessian of the D-gap function and Newton-type methods for variational inequality problems
    • M. Ferris and J.-S. Pang, eds., SIAM, Philadelphia, PA
    • D. SUN, M. FUKUSHIMA, AND L. QI, A computable generalized Hessian of the D-gap function and Newton-type methods for variational inequality problems, in Complementarity and Variational Problems: State of the Art, M. Ferris and J.-S. Pang, eds., SIAM, Philadelphia, PA, 1997, pp. 452-473.
    • (1997) Complementarity and Variational Problems: State of the Art , pp. 452-473
    • Sun, D.1    Fukushima, M.2    Qi, L.3
  • 50
    • 0008973240 scopus 로고
    • Optimization based globally convergent methods for the nonlinear complementarity problems
    • K. TAJI AND M. FUKUSHIMA, Optimization based globally convergent methods for the nonlinear complementarity problems, J. Oper. Res. Soc. Japan, 37 (1994), pp. 310-331.
    • (1994) J. Oper. Res. Soc. Japan , vol.37 , pp. 310-331
    • Taji, K.1    Fukushima, M.2
  • 51
    • 0027543289 scopus 로고
    • A globally convergent Newton method for solving strongly monotone variational inequalities
    • K. TAJI, M. FUKUSHIMA, AND T. IBARAKI, A globally convergent Newton method for solving strongly monotone variational inequalities, Math. Programming, 58 (1993), pp. 369-383.
    • (1993) Math. Programming , vol.58 , pp. 369-383
    • Taji, K.1    Fukushima, M.2    Ibaraki, T.3
  • 52
    • 34250082175 scopus 로고
    • A general descent framework for the monotone variational inequality problem
    • J. WU, M. FLORIAN, AND P. MARCOTTE, A general descent framework for the monotone variational inequality problem, Math. Programming, 61 (1993), pp. 281-300.
    • (1993) Math. Programming , vol.61 , pp. 281-300
    • Wu, J.1    Florian, M.2    Marcotte, P.3
  • 53
    • 0000116396 scopus 로고    scopus 로고
    • Modified Newton methods for solving a semismooth reformulation of monotone complementarity problems
    • N. YAMASHITA AND M. FUKUSHIMA, Modified Newton methods for solving a semismooth reformulation of monotone complementarity problems, Math. Programming, 76 (1997), pp. 469-491.
    • (1997) Math. Programming , vol.76 , pp. 469-491
    • Yamashita, N.1    Fukushima, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.