메뉴 건너뛰기




Volumn 8, Issue 1, 1998, Pages 140-157

A trust region method for solving generalized complementarity problems

Author keywords

Generalized complementarity problem; Global and superlinear convergence; Nonlinear complementarity problem; Semismooth equation; Trust region method

Indexed keywords


EID: 0032331517     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623495296541     Document Type: Article
Times cited : (63)

References (35)
  • 1
    • 0030648154 scopus 로고    scopus 로고
    • A comparison of large scale mixed complementarity problem solvers
    • S. C. BILLUPS, S. P. DIRKSE, AND M. C. FERRIS, A comparison of large scale mixed complementarity problem solvers, Comput. Optim. Appl., 7 (1997), pp. 3-25.
    • (1997) Comput. Optim. Appl. , vol.7 , pp. 3-25
    • Billups, S.C.1    Dirkse, S.P.2    Ferris, M.C.3
  • 2
    • 0030104686 scopus 로고    scopus 로고
    • A class of smoothing functions for nonlinear and mixed complementarity problems
    • C. CHEN AND O. L. MANGASARIAN, A class of smoothing functions for nonlinear and mixed complementarity problems, Comput. Optim. Appl., 5 (1996), pp. 97-138.
    • (1996) Comput. Optim. Appl. , vol.5 , pp. 97-138
    • Chen, C.1    Mangasarian, O.L.2
  • 5
    • 0043189808 scopus 로고    scopus 로고
    • A semismooth equation approach to the solution of nonlinear complementarity problems
    • T. DE 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
    • De Luca, T.1    Facchinei, F.2    Kanzow, C.3
  • 6
    • 0029423693 scopus 로고
    • The PATH solver: A non-monotone stabilization scheme for mixed complementarity problems
    • S. P. DIRKSE AND M. C. FERRIS, The PATH solver: A non-monotone stabilization scheme for mixed complementarity problems, Optimization Methods and Software, 5 (1995), pp. 123-156.
    • (1995) Optimization Methods and Software , vol.5 , pp. 123-156
    • Dirkse, S.P.1    Ferris, M.C.2
  • 7
    • 0029425015 scopus 로고
    • MCPLIB: A collection of nonlinear mixed complementarity problems
    • S. P. DIRKSE AND M. C. FERRIS, MCPLIB: A collection of nonlinear mixed complementarity problems, Optimization Methods and Software, 5 (1995), pp. 319-345.
    • (1995) Optimization Methods and Software , vol.5 , pp. 319-345
    • Dirkse, S.P.1    Ferris, M.C.2
  • 8
    • 0003117688 scopus 로고
    • Implicit complementarity problems and quasi-variational inequalities
    • R. W. Cottle, F. Giannessi, and J.-L. Lions, eds., Wiley, New York
    • I. C. DOLCETTA AND U. MOSCO, Implicit complementarity problems and quasi-variational inequalities, in Variational Inequalities and Complementarity Problems: Theory and Applications, R. W. Cottle, F. Giannessi, and J.-L. Lions, eds., Wiley, New York, 1980, pp. 75-87.
    • (1980) Variational Inequalities and Complementarity Problems: Theory and Applications , pp. 75-87
    • Dolcetta, I.C.1    Mosco, U.2
  • 9
    • 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
  • 10
    • 0039332368 scopus 로고    scopus 로고
    • Accessing realistic mixed complementarity problems within MATLAB
    • G. Di Pillo and F. Giannessi, eds., Plenum Press, New York
    • M. C. FERRIS AND T. F. RUTHERFORD, Accessing realistic mixed complementarity problems within MATLAB, in Nonlinear Optimization and Applications, G. Di Pillo and F. Giannessi, eds., Plenum Press, New York, 1996, pp. 141-153.
    • (1996) Nonlinear Optimization and Applications , pp. 141-153
    • Ferris, M.C.1    Rutherford, T.F.2
  • 11
    • 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
  • 12
    • 0002132714 scopus 로고
    • An NCP-function and its use for the solution of complementarity problems
    • D. Du. L. Qi, and R. Womersley, eds., World Scientific Publishers, River Edge, NJ
    • A. FISCHER, An NCP-function and its use for the solution of complementarity problems, in Recent Advances in Nonsmooth Optimization, D. Du. L. Qi, and R. Womersley, eds., World Scientific Publishers, River Edge, NJ, 1995, pp. 88-105.
    • (1995) Recent Advances in Nonsmooth Optimization , pp. 88-105
    • Fischer, A.1
  • 13
    • 0000554369 scopus 로고    scopus 로고
    • Solution of monotone complementarity problems with locally lipschitzian functions
    • A. FISCHER, Solution of monotone complementarity problems with locally Lipschitzian functions, Math. Programming, 76 (1997), pp. 513-532.
    • (1997) Math. Programming , vol.76 , pp. 513-532
    • Fischer, A.1
  • 15
    • 0002358032 scopus 로고    scopus 로고
    • Merit functions for variational inequality and complementarity problems
    • G. Di 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. Di Pillo and F. Giannessi, eds., Plenum Press, New York, 1996, pp. 155-170.
    • (1996) Nonlinear Optimization and Applications , pp. 155-170
    • Fukushima, M.1
  • 16
    • 0002560226 scopus 로고    scopus 로고
    • Minimizing and stationary sequences of merit functions for complementarity problems and variational inequalities
    • M. C. Ferris and J.-S. Pang, eds., SIAM, Philadelphia, PA
    • M. FUKUSHIMA AND J.-S. PANG, Minimizing and stationary sequences of merit functions for complementarity problems and variational inequalities, in Complementarity and Variational Problems: State of the Art, M. C. Ferris and J.-S. Pang, eds., SIAM, Philadelphia, PA, 1997, pp. 91-104.
    • (1997) Complementarity and Variational Problems: State of the Art , pp. 91-104
    • Fukushima, M.1    Pang, J.-S.2
  • 17
    • 0013111241 scopus 로고
    • A trust region method for constrained nonsmooth equations
    • W. W. Hager, D. W. Hearn, and P. M. Pardalos, eds., Kluwer Academic Publishers, Boston. MA
    • S. A. GABRIEL AND J.-S. PANG, A trust region method for constrained nonsmooth equations, in Large Scale Optimization: State of the Art, W. W. Hager, D. W. Hearn, and P. M. Pardalos, eds., Kluwer Academic Publishers, Boston. MA, 1994, pp. 159-186.
    • (1994) Large Scale Optimization: State of the Art , pp. 159-186
    • Gabriel, S.A.1    Pang, J.-S.2
  • 18
    • 0344704362 scopus 로고
    • Finite-dimensional variational inequality and nonlinear complementarity problem: A survey of theory, algorithms and applications
    • P. T. HARKER AND J.-S. PANG, Finite-dimensional variational inequality and nonlinear complementarity problem: A survey of theory, algorithms and applications, Math. Programming, 48 (1990), pp. 161-220.
    • (1990) Math. Programming , vol.48 , pp. 161-220
    • Harker, P.T.1    Pang, J.-S.2
  • 19
    • 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
  • 20
    • 0030524071 scopus 로고    scopus 로고
    • Equivalence of the generalized complementarity problem to differentiable unconstrained minimization
    • C. KANZOW AND M. FUKUSHIMA, Equivalence of the generalized complementarity problem to differentiable unconstrained minimization, J. Optim. Theory Appl., 90 (1996), pp. 581-603.
    • (1996) J. Optim. Theory Appl. , vol.90 , pp. 581-603
    • Kanzow, C.1    Fukushima, M.2
  • 21
    • 0039189400 scopus 로고    scopus 로고
    • Theoretical and numerical investigation of the D-gap function for box constrained variational inequalities
    • to appear
    • C. KANZOW AND M. FUKUSHIMA, Theoretical and numerical investigation of the D-gap function for box constrained variational inequalities, Math. Programming, to appear.
    • Math. Programming
    • Kanzow, C.1    Fukushima, M.2
  • 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
    • 34249768673 scopus 로고
    • A trust region strategy for minimization on arbitrary domains
    • J. M. MARTÍNEZ AND A. SANTOS, A trust region strategy for minimization on arbitrary domains, Math. Programming, 68 (1995), pp. 267-302.
    • (1995) Math. Programming , vol.68 , pp. 267-302
    • Martínez, J.M.1    Santos, A.2
  • 24
    • 0000012763 scopus 로고
    • Semismooth and semiconvex functions in constrained optimization
    • R. MIFFLIN, Semismooth and semiconvex functions in constrained optimization, SIAM J. Control Optim., 15 (1977), pp. 959-972.
    • (1977) SIAM J. Control Optim. , vol.15 , pp. 959-972
    • Mifflin, R.1
  • 25
    • 0003162836 scopus 로고
    • Recent developments in algorithms and software for trust region methods
    • A. Bachem, M. Grötschel, and B. Korte, eds., Springer-Verlag, Berlin
    • J. J. MORÉ, Recent developments in algorithms and software for trust region methods, in Mathematical Programming: The State of the Art, A. Bachem, M. Grötschel, and B. Korte, eds., Springer-Verlag, Berlin, 1983, pp. 258-287.
    • (1983) Mathematical Programming: The State of the Art , pp. 258-287
    • Moré, J.J.1
  • 26
    • 0030204920 scopus 로고    scopus 로고
    • Global methods for nonlinear complementarity problems
    • J. J. MORÉ, Global methods for nonlinear complementarity problems, Math. Oper. Res., 21 (1996), pp. 589-614.
    • (1996) Math. Oper. Res. , vol.21 , pp. 589-614
    • Moré, J.J.1
  • 27
    • 0009969104 scopus 로고
    • A Newton method for a class of quasi-variational inequalities
    • J. V. OUTRATA AND J. ZOWE, A Newton method for a class of quasi-variational inequalities, Comput. Optim. Appl., 4 (1995), pp. 5-21.
    • (1995) Comput. Optim. Appl. , vol.4 , pp. 5-21
    • Outrata, J.V.1    Zowe, J.2
  • 28
    • 0000804782 scopus 로고
    • The implicit complementarity problem
    • O. L. Mangasarian, S. M. Robinson, and R. R. Meyer, eds., Academic Press, New York
    • J.-S. PANG, The implicit complementarity problem, in Nonlinear Programming 4, O. L. Mangasarian, S. M. Robinson, and R. R. Meyer, eds., Academic Press, New York, 1981, pp. 487-518.
    • (1981) Nonlinear Programming , vol.4 , pp. 487-518
    • Pang, J.-S.1
  • 29
    • 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
  • 30
    • 34250083447 scopus 로고
    • NE/SQP: A robust algorithm for the nonlinear complementarity problem
    • J.-S. PANG AND S. A. GABRIEL, NE/SQP: A robust algorithm for the nonlinear complementarity problem, Math. Programming, 60 (1993), pp. 295-337.
    • (1993) Math. Programming , vol.60 , pp. 295-337
    • Pang, J.-S.1    Gabriel, S.A.2
  • 31
    • 0002302301 scopus 로고
    • Convergence properties of a class of minimization algorithms
    • O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, eds., Academic Press, New York
    • M. J. D. POWELL, Convergence properties of a class of minimization algorithms, in Nonlinear Programming 2, O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, eds., Academic Press, New York, 1975, pp. 1-27.
    • (1975) Nonlinear Programming , vol.2 , pp. 1-27
    • Powell, M.J.D.1
  • 32
    • 0000607524 scopus 로고
    • Convergence analysis of some algorithms for solving nonsmooth equations
    • L. QI, Convergence analysis of some algorithms for solving nonsmooth equations, Math. Oper. Res., 18 (1993), pp. 227-244.
    • (1993) Math. Oper. Res. , vol.18 , pp. 227-244
    • Qi, L.1
  • 33
    • 0027543961 scopus 로고
    • A nonsmooth version of Newton's method
    • L. QI AND J. SUN, A nonsmooth version of Newton's method, Math. Programming, 58 (1993), pp. 353-368.
    • (1993) Math. Programming , vol.58 , pp. 353-368
    • Qi, L.1    Sun, J.2
  • 34
    • 0002939936 scopus 로고
    • Generalized equations
    • A. Bachem, M. Grötschel, and B. Korte, eds., Springer-Verlag, Berlin
    • S. M. ROBINSON, Generalized equations, in Mathematical Programming: The State of the Art, A. Bachem, M. Grötschel, and B. Korte, eds., Springer-Verlag, Berlin, 1983, pp. 346-367.
    • (1983) Mathematical Programming: The State of the Art , pp. 346-367
    • Robinson, S.M.1
  • 35
    • 0030303845 scopus 로고    scopus 로고
    • Equivalence of complementarity problems to differentiable minimization: A unified approach
    • P. TSENG, N. YAMASHITA, AND M. FUKUSHIMA, Equivalence of complementarity problems to differentiable minimization: A unified approach, SIAM J. Optim., 6 (1996), pp. 446-460.
    • (1996) SIAM J. Optim. , vol.6 , pp. 446-460
    • Tseng, P.1    Yamashita, N.2    Fukushima, M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.