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Volumn 21, Issue 3, 1996, Pages 589-614

Global methods for nonlinear complementarity problems

Author keywords

Convergence; Nonlinear complementarity; Nonlinear least squares

Indexed keywords

ALGORITHMS; CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; DYNAMIC PROGRAMMING; ITERATIVE METHODS; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL TRANSFORMATIONS; OPTIMIZATION; PROBLEM SOLVING;

EID: 0030204920     PISSN: 0364765X     EISSN: None     Source Type: Journal    
DOI: 10.1287/moor.21.3.589     Document Type: Article
Times cited : (69)

References (51)
  • 2
    • 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
  • 3
    • 70350657102 scopus 로고
    • Least squares methods
    • P. G. Ciarlet and J. L. Lions, Eds., City, North-Holland
    • Björck, A. (1990). Least squares methods. P. G. Ciarlet and J. L. Lions, Eds., Handbook of Numerical Analysis, City, North-Holland, 465-647.
    • (1990) Handbook of Numerical Analysis , pp. 465-647
    • Björck, A.1
  • 4
    • 33747796524 scopus 로고
    • Convergence properties of trust region methods for linear and convex constraints
    • Burke, J. V., J. J. Moré and G. Toraldo (1990). Convergence properties of trust region methods for linear and convex constraints. Math. Programming 47 305-336.
    • (1990) Math. Programming , vol.47 , pp. 305-336
    • Burke, J.V.1    Moré, J.J.2    Toraldo, G.3
  • 5
    • 0001067548 scopus 로고
    • A continuation method for monotone variational inequalities
    • Chen, B. and P. T. Harker (1995). A continuation method for monotone variational inequalities. Math. Programming 69 237-253.
    • (1995) Math. Programming , vol.69 , pp. 237-253
    • Chen, B.1    Harker, P.T.2
  • 6
    • 0010765575 scopus 로고
    • An interior trust region approach for nonlinear minimization subject to bounds
    • Cornell University, Ithaca, NY
    • Coleman, T. F. and Y. Li (1993). An interior trust region approach for nonlinear minimization subject to bounds. Technical report 93-1342, Cornell University, Ithaca, NY.
    • (1993) Technical Report 93-1342
    • Coleman, T.F.1    Li, Y.2
  • 7
    • 0002467356 scopus 로고
    • Global convergence of a class of trust region algorithms for optimization problems with simple bounds
    • Conn, A. R. N. I. N. Gould and P. L. Toint (1988a). Global convergence of a class of trust region algorithms for optimization problems with simple bounds. SIAM J. Numerical Analysis 25 433-460.
    • (1988) SIAM J. Numerical Analysis , vol.25 , pp. 433-460
    • Conn, A.R.1    Gould, N.I.N.2    Toint, P.L.3
  • 8
    • 84966215545 scopus 로고
    • Testing a class of methods for solving minimization problems with simple bounds on the variables
    • _, _ and _ (1988b). Testing a class of methods for solving minimization problems with simple bounds on the variables. Math. Comp. 50 399-430.
    • (1988) Math. Comp. , vol.50 , pp. 399-430
  • 10
    • 0029423693 scopus 로고
    • The PATH solver: A non-monotone stabilization scheme for mixed complementarity problems
    • Dirkse, S. P. and M. C. Ferris (1995a). The PATH solver: A non-monotone stabilization scheme for mixed complementarity problems. Optim. Methods Software 5 123-156.
    • (1995) Optim. Methods Software , vol.5 , pp. 123-156
    • Dirkse, S.P.1    Ferris, M.C.2
  • 11
    • 0029425015 scopus 로고
    • MCPLIB: A collection of nonlinear mixed complementarity problems
    • _ and _ (1995b). MCPLIB: A collection of nonlinear mixed complementarity problems. Optim. Methods Software 5 319-345.
    • (1995) Optim. Methods Software , vol.5 , pp. 319-345
  • 12
    • 0000803454 scopus 로고
    • On matrices with non-positive off-diagonal elements and positive principal minors
    • Fiedler, M. and V. Pták (1962). On matrices with non-positive off-diagonal elements and positive principal minors. Czech. Math. J. 12 382-400.
    • (1962) Czech. Math. J. , vol.12 , pp. 382-400
    • Fiedler, M.1    Pták, V.2
  • 13
    • 0001326068 scopus 로고
    • Some generalizations of positive definiteness and monotonicity
    • _ and _ (1966). Some generalizations of positive definiteness and monotonicity. Numer. Mathematics 9 163-172.
    • (1966) Numer. Mathematics , vol.9 , pp. 163-172
  • 14
    • 84968452648 scopus 로고
    • Iterative solution of linear systems
    • A. Iserles, Ed., Cambridge University Press, City
    • Freund, R. W., G. H. Golub and N. M. Nachtigal (1992). Iterative solution of linear systems. A. Iserles, Ed., Acta Numerica 1992, Cambridge University Press, City, 57-100.
    • (1992) Acta Numerica 1992 , pp. 57-100
    • Freund, R.W.1    Golub, G.H.2    Nachtigal, N.M.3
  • 15
    • 0026763569 scopus 로고
    • Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems
    • Fukushima, M. (1992). Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems. Math. Programming 53 99-110.
    • (1992) Math. Programming , vol.53 , pp. 99-110
    • Fukushima, M.1
  • 16
    • 0001867697 scopus 로고
    • An inexact NE/SQP method for solving the nonlinear complementarity problem
    • Gabriel, S. A. and J. S. Pang (1992). An inexact NE/SQP method for solving the nonlinear complementarity problem. Comp. Optim. Appl. 1 67-91.
    • (1992) Comp. Optim. Appl. , vol.1 , pp. 67-91
    • Gabriel, S.A.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, Inc.
    • _ and _ (1993). A trust region method for constrained nonsmooth equations. W. W. Hager, D. W. Hearn and P. M. Pardalos, Eds., Large-Scale Optimization: State of the Art, Kluwer Academic Publishers, Inc.
    • (1993) Large-Scale Optimization: State of the Art
  • 18
    • 0002105392 scopus 로고
    • A trust region approach to linearly constrained optimization
    • D. F. Griffiths, Ed-, Lecture Notes in Mathematics 1066, Springer-Verlag, Berlin
    • Gay, D. M. (1984). A trust region approach to linearly constrained optimization. D. F. Griffiths, Ed-, Numerical Analysis, Lecture Notes in Mathematics 1066, Springer-Verlag, Berlin, 72-105.
    • (1984) Numerical Analysis , pp. 72-105
    • Gay, D.M.1
  • 20
    • 0344704362 scopus 로고
    • Finite dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications
    • Harker, P. T. and J. S. Pang (1990). Finite dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Math. Programming 18 161-220.
    • (1990) Math. Programming , vol.18 , pp. 161-220
    • Harker, P.T.1    Pang, J.S.2
  • 21
    • 34249962655 scopus 로고
    • Newton's method for the nonlinear complementarity problem: A B-differentiable equation problem
    • _ and B. Xiao (1990). Newton's method for the nonlinear complementarity problem: A B-differentiable equation problem. Math. Programming 48 339-357.
    • (1990) Math. Programming , vol.48 , pp. 339-357
    • Xiao, B.1
  • 24
    • 0007710807 scopus 로고
    • A general framework of continuation method for complementarity problems
    • Kojima, M., N. Megiddo and S. Mizuno (1993). A general framework of continuation method for complementarity problems. Math. Oper. Res. 18 945-963.
    • (1993) Math. Oper. Res. , vol.18 , pp. 945-963
    • Kojima, M.1    Megiddo, N.2    Mizuno, S.3
  • 25
    • 0001217295 scopus 로고
    • Homotopy continuation methods for nonlinear complementarity problems
    • _, _ and T. Noma (1991). Homotopy continuation methods for nonlinear complementarity problems. Math. Oper. Res. 16 754-774.
    • (1991) Math. Oper. Res. , vol.16 , pp. 754-774
    • Noma, T.1
  • 26
    • 0024303530 scopus 로고
    • A new continuation method for complementarity problems with uniform P-functions
    • _, S. Mizuno and T. Noma (1989). A new continuation method for complementarity problems with uniform P-functions. Math. Programming 43 107-113.
    • (1989) Math. Programming , vol.43 , pp. 107-113
    • Mizuno, S.1    Noma, T.2
  • 27
    • 0001214560 scopus 로고
    • Limiting behavior of trajectories generated by a continuation method for monotone complementarity problems
    • _, _ and _ (1990). Limiting behavior of trajectories generated by a continuation method for monotone complementarity problems. Math. Oper. Res. 15 662-675.
    • (1990) Math. Oper. Res. , vol.15 , pp. 662-675
  • 28
    • 5744226067 scopus 로고
    • Global convergence in infeasible interior point algorithms
    • _, _ and A. Yoshise (1994). Global convergence in infeasible interior point algorithms. Math. Programming 65 43-72.
    • (1994) Math. Programming , vol.65 , pp. 43-72
    • Yoshise, A.1
  • 29
    • 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. SJAM J. Numer. Anal. 28 476-495.
    • (1991) SJAM J. Numer. Anal. , vol.28 , pp. 476-495
    • Lescrenier, M.1
  • 30
    • 0002147441 scopus 로고
    • Equivalence of the complementarity problem to a system of nonlinear equations
    • Mangasarian, O. L. (1976). Equivalence of the complementarity problem to a system of nonlinear equations, SIAM J. Appl. Math. 31 89-92.
    • (1976) SIAM J. Appl. Math. , vol.31 , pp. 89-92
    • Mangasarian, O.L.1
  • 31
    • 34250076671 scopus 로고
    • Nonlinear complementarity as unconstrained and constrained minimization
    • _ and M. V. Solodov (1993). Nonlinear complementarity as unconstrained and constrained minimization. Math. Programming 62 277-297.
    • (1993) Math. Programming , vol.62 , pp. 277-297
    • Solodov, M.V.1
  • 33
    • 0002497386 scopus 로고
    • The complementarity problem for maximal monotone multifunctions
    • R. W. Cottle, F. Giannessi and J.-L. Lions, Eds., John Wiley & Sons, New York
    • McLinden, L. (1980). The complementarity problem for maximal monotone multifunctions. R. W. Cottle, F. Giannessi and J.-L. Lions, Eds., Variational Inequalities and Complementarity Problems, John Wiley & Sons, New York, 251-268.
    • (1980) Variational Inequalities and Complementarity Problems , pp. 251-268
    • McLinden, L.1
  • 34
    • 0040470024 scopus 로고
    • A positive algorithm for the nonlinear complementarity problem
    • Monteiro, R. D. C., J. S. Pang and T. Wang (1995). A positive algorithm for the nonlinear complementarity problem. SIAM J. Optim. 5 129-148.
    • (1995) SIAM J. Optim. , vol.5 , pp. 129-148
    • Monteiro, R.D.C.1    Pang, J.S.2    Wang, T.3
  • 35
    • 0016071184 scopus 로고
    • Classes of function and feasibility conditions in nonlinear complementarity problems
    • Moré, J. J. (1974a). Classes of function and feasibility conditions in nonlinear complementarity problems. Math. Programming 6 327-338.
    • (1974) Math. Programming , vol.6 , pp. 327-338
    • Moré, J.J.1
  • 36
    • 0015982712 scopus 로고
    • Coercivity conditions in nonlinear complementarity problems
    • _ (1974b). Coercivity conditions in nonlinear complementarity problems. SIAM Rev. 16 1-16.
    • (1974) SIAM Rev. , vol.16 , pp. 1-16
  • 37
    • 0002565002 scopus 로고
    • On P- and S-functions and related classes of n-dimensional mappings
    • _ and W. C. Rheinboldt (1973). On P- and S-functions and related classes of n-dimensional mappings. Linear Algebra Appl. 6 45-68.
    • (1973) Linear Algebra Appl. , vol.6 , pp. 45-68
    • Rheinboldt, W.C.1
  • 38
    • 33845418028 scopus 로고
    • On the solution of large quadratic programming problems with bound constraints
    • _ and G. Toraldo (1991). On the solution of large quadratic programming problems with bound constraints. SIAM J. Optimization 1 93-113.
    • (1991) SIAM J. Optimization , vol.1 , pp. 93-113
    • Toraldo, G.1
  • 41
    • 0001601094 scopus 로고
    • Newton's method for B-differentiable equations
    • Pang, J. S. (1990). Newton's method for B-differentiable equations. Math. Oper. Res. 15 311-341.
    • (1990) Math. Oper. Res. , vol.15 , pp. 311-341
    • Pang, J.S.1
  • 42
    • 34250083447 scopus 로고
    • NE/SQP: A robust algorithm for the nonlinear complementarity problem
    • _ and S. A. Gabriel (1993). NE/SQP: A robust algorithm for the nonlinear complementarity problem. Math. Programming 60 295-337.
    • (1993) Math. Programming , vol.60 , pp. 295-337
    • Gabriel, S.A.1
  • 43
    • 0001393203 scopus 로고
    • Global convergence of damped Newton's method for nonsmooth equations via the path search
    • Ralph, D. (1994). Global convergence of damped Newton's method for nonsmooth equations via the path search. Math. Oper. Res. 19 352-389.
    • (1994) Math. Oper. Res. , vol.19 , pp. 352-389
    • Ralph, D.1
  • 44
    • 0001272077 scopus 로고
    • Normal maps induced by linear transformations
    • Robinson, S. M. (1992). Normal maps induced by linear transformations. Math. Oper. Res. 17 691-714.
    • (1992) Math. Oper. Res. , vol.17 , pp. 691-714
    • Robinson, S.M.1
  • 45
    • 0039332292 scopus 로고
    • An active set Newton's method for large-scale nonlinear programs with box constraints
    • IASI-CNR, Rome, Italy
    • Soares, J., J. Júdice and F. Facchinei (1993). An active set Newton's method for large-scale nonlinear programs with box constraints. Technical Report 367, IASI-CNR, Rome, Italy.
    • (1993) Technical Report 367
    • Soares, J.1    Júdice, J.2    Facchinei, F.3
  • 46
    • 0027609382 scopus 로고
    • Gauss-Newton methods for complementarity problems
    • Subramanian, P. K. (1993). Gauss-Newton methods for complementarity problems. J. Optim. Theory Appl. 77 467-482.
    • (1993) J. Optim. Theory Appl. , vol.77 , pp. 467-482
    • Subramanian, P.K.1
  • 47
    • 0001784299 scopus 로고
    • Solving the nonlinear complementarity problem by a homotopy method
    • Watson, L. T. (1976). Solving the nonlinear complementarity problem by a homotopy method. SIAM J. Control Optim. 17 36-46.
    • (1976) SIAM J. Control Optim. , vol.17 , pp. 36-46
    • Watson, L.T.1
  • 49
    • 0039014262 scopus 로고
    • Stability of linear equations solvers in interior-point methods
    • _ (1994). Stability of linear equations solvers in interior-point methods. SIAM J. Matrix Anal. Appl. 16 1287-1307.
    • (1994) SIAM J. Matrix Anal. Appl. , vol.16 , pp. 1287-1307
  • 50
    • 0028442796 scopus 로고
    • A nonsmooth Newton method for variational inequalities, I: Theory
    • Xiao, B. and P. T. Harker (1994a). A nonsmooth Newton method for variational inequalities, I: Theory. Math. Programming 65 151-194.
    • (1994) Math. Programming , vol.65 , pp. 151-194
    • Xiao, B.1    Harker, P.T.2
  • 51
    • 0028443257 scopus 로고
    • A nonsmooth Newton method for variational inequalities, II: Numerical Results
    • _ and _ (1994b). A nonsmooth Newton method for variational inequalities, II: Numerical Results. Math. Programming 65 195-216.
    • (1994) Math. Programming , vol.65 , pp. 195-216


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