메뉴 건너뛰기




Volumn 19, Issue 3, 2008, Pages 1028-1047

A regularized smoothing Newton method for symmetric cone complementarity problems

Author keywords

Monotonicity; Natural residual function; Quadratic convergence; Regularized smoothing method; Symmetric cone complementarity problem

Indexed keywords

MONOTONICITY; NATURAL RESIDUAL FUNCTION; QUADRATIC CONVERGENCE; REGULARIZED SMOOTHING METHOD; SYMMETRIC CONE COMPLEMENTARITY PROBLEM;

EID: 60749104020     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/060676775     Document Type: Article
Times cited : (74)

References (37)
  • 1
    • 21344485287 scopus 로고
    • A non-interior-point continuation method for linear complementarity problems
    • B. Chen and P. T. Harker, A non-interior-point continuation method for linear complementarity problems, SIAM J. Matrix Anal. Appl., 14 (1993), pp. 1168-1190.
    • (1993) SIAM. J. Matrix Anal. Appl. , vol.14 , pp. 1168-1190
    • Chen, B.1    Harker, P.T.2
  • 2
    • 0029206129 scopus 로고
    • Smoothing methods for convex inequalities and linear complementarity problems
    • C. Chen and O. L. Mangasarian, Smoothing methods for convex inequalities and linear complementarity problems, Math. Program., 71 (1995), pp. 51-69.
    • (1995) Math. Program. , vol.71 , pp. 51-69
    • Chen, C.1    Mangasarian, O.L.2
  • 3
    • 27244436420 scopus 로고    scopus 로고
    • An unconstrained smooth minimization reformulation of the secondorder cone complementarity problem
    • J.-S. Chen and P. Tseng, An unconstrained smooth minimization reformulation of the secondorder cone complementarity problem, Math. Program. Ser. B, 104 (2005), pp. 293-327.
    • (2005) Math. Program. Ser. B. , vol.104 , pp. 293-327
    • Chen, J.-S.1    Tseng, P.2
  • 4
    • 29144505119 scopus 로고    scopus 로고
    • Cartesian P-property and its applications to the semidefinite linear complementarity problem
    • X. Chen and H. D. Qi, Cartesian P-property and its applications to the semidefinite linear complementarity problem, Math. Program., 106 (2006), pp. 177-201.
    • (2006) Math. Program. , vol.106 , pp. 177-201
    • Chen, X.1    Qi, H.D.2
  • 5
    • 0038485144 scopus 로고    scopus 로고
    • Analysis of nonsmooth symmetric matrix functions with applications to semidefinite complementarity problems
    • X. Chen, H. D. Qi, and P. Tseng, Analysis of nonsmooth symmetric matrix functions with applications to semidefinite complementarity problems, SIAM J. Optim., 13 (2003), pp. 960-985.
    • (2003) SIAM. J. Optim. , vol.13 , pp. 960-985
    • Chen, X.1    Qi, H.D.2    Tseng, P.3
  • 6
    • 0346405888 scopus 로고    scopus 로고
    • Non-interior continuation methods for solving semidefinite complementarity problems
    • X. Chen and P. Tseng, Non-interior continuation methods for solving semidefinite complementarity problems, Math. Program., 95 (2003), pp. 431-474.
    • (2003) Math. Program. , vol.95 , pp. 431-474
    • Chen, X.1    Tseng, P.2
  • 7
    • 0037391603 scopus 로고    scopus 로고
    • Complementarity functions and numerical experiments on some smoothing Newton methods for second-order-cone complementarity problems
    • X. D. Chen, D. Sun, and J. Sun, Complementarity functions and numerical experiments on some smoothing Newton methods for second-order-cone complementarity problems, Cornput. Optim. Appl., 25 (2003), pp. 39-56.
    • (2003) Cornput. Optim. Appl. , vol.25 , pp. 39-56
    • Chen, X.D.1    Sun, D.2    Sun, J.3
  • 8
    • 0032380644 scopus 로고    scopus 로고
    • Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities
    • X. J. Chen, L. Qi, and D. Sun, Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities, Math. Comput., 67 (1998), pp. 519-540.
    • (1998) Math. Comput. , vol.67 , pp. 519-540
    • Chen, X.J.1    Qi, L.2    Sun, D.3
  • 11
    • 0036013023 scopus 로고    scopus 로고
    • Smoothing functions for second-order cone complementarity problems
    • M. Fukushima, Z. Q. Luo, and P. Tseng, Smoothing functions for second-order cone complementarity problems, SIAM J. Optim., 12 (2001), pp. 436-460.
    • (2001) SIAM. J. Optim. , vol.12 , pp. 436-460
    • Fukushima, M.1    Luo, Z.Q.2    Tseng, P.3
  • 12
    • 7444231047 scopus 로고    scopus 로고
    • Some P-properties for linear transformations on Euclidean Jordan algebras
    • M. S. Gowda, R. Sznajder, and J. Tao, Some P-properties for linear transformations on Euclidean Jordan algebras, Linear Algebra Appl., 393 (2004), pp. 203-232.
    • (2004) Linear Algebra Appl. , vol.393 , pp. 203-232
    • Gowda, M.S.1    Sznajder, R.2    Tao, J.3
  • 13
    • 33646735464 scopus 로고    scopus 로고
    • Automorphism invariance of p and GUS properties of linear transformations on Euclidean Jordan algebras
    • M. S. Gowda and R. Sznajder, Automorphism invariance of P and GUS properties of linear transformations on Euclidean Jordan algebras, Math. Oper. Res., 31 (2006), pp. 109-123.
    • (2006) Math. Oper. Res. , vol.31 , pp. 109-123
    • Gowda, M.S.1    Sznajder, R.2
  • 14
    • 44649116496 scopus 로고    scopus 로고
    • Some global uniqueness and solvability results for linear complementarity problems over symmetric cones
    • M. S. Gowda and R. Sznajder, Some global uniqueness and solvability results for linear complementarity problems over symmetric cones, SIAM J. Optim., 18 (2007), pp. 461-481.
    • (2007) SIAM. J. Optim. , vol.18 , pp. 461-481
    • Gowda, M.S.1    Sznajder, R.2
  • 15
    • 18744383641 scopus 로고    scopus 로고
    • A combined smoothing and regularization method for monotone second-order cone complementarity problems
    • S. Hayashi, N. Yamashita, and M. Fukushima, A combined smoothing and regularization method for monotone second-order cone complementarity problems, SIAM J. Optim., 15 (2005), pp. 593-615.
    • (2005) SIAM. J. Optim. , vol.15 , pp. 593-615
    • Hayashi, S.1    Yamashita, N.2    Fukushima, M.3
  • 16
    • 0348163537 scopus 로고    scopus 로고
    • Non-interior continuation method for solving the monotone semidefinite complementarity problem
    • Z. H. Huang and J. HAN, Non-interior continuation method for solving the monotone semidefinite complementarity problem, Appl. Math. Optim., 47 (2003), pp. 195-211.
    • (2003) Appl. Math. Optim. , vol.47 , pp. 195-211
    • Huang, Z.H.1    Han, J.2
  • 18
    • 0030517292 scopus 로고    scopus 로고
    • Some noninterior continuation methods for linear complementarity problems
    • C. KANZOW, Some noninterior continuation methods for linear complementarity problems, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 851-868.
    • (1996) SIAM. J. Matrix Anal. Appl. , vol.17 , pp. 851-868
    • Kanzow, C.1
  • 21
    • 34250967722 scopus 로고
    • Über monotone matrixfunctionen
    • K. Löwner, Über monotone matrixfunctionen, Math. Z., 38 (1934), pp. 177-216.
    • (1934) Math. Z. , vol.38 , pp. 177-216
    • Löwner, K.1
  • 22
    • 33846311381 scopus 로고    scopus 로고
    • Some properties of a class of merit functions for symmetric cone complementarity problems
    • Y. Liu, L. Zhang, and Y. Wang, Some properties of a class of merit functions for symmetric cone complementarity problems, Asia-Pacific J. Oper. Res., 23 (2006), pp. 473-496.
    • (2006) Asia-Pacific J. Oper. Res. , vol.23 , pp. 473-496
    • Liu, Y.1    Zhang, L.2    Wang, Y.3
  • 23
    • 29144464966 scopus 로고    scopus 로고
    • Cone complementarity problems with finite solution sets
    • M. Malik and S. R. Mohan, Cone complementarity problems with finite solution sets, Oper. Res. Lett., 34 (2006), pp. 121-126.
    • (2006) Oper. Res. Lett. , vol.34 , pp. 121-126
    • Malik, M.1    Mohan, S.R.2
  • 24
    • 0000012763 scopus 로고
    • Semismooth and semiconvex functions in constrained optimization
    • R. Mifflin, Semismooth and semiconvex functions in constrained optimization, SIAM J. Cont. Optim., 15 (1977), pp. 959-972.
    • (1977) SIAM. J. Cont. Optim. , vol.15 , pp. 959-972
    • Mifflin, R.1
  • 25
    • 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. Program., 86 (1999), pp. 367-386.
    • (1999) Math. Program. , vol.86 , pp. 367-386
    • Peng, J.M.1    Fukushima, M.2
  • 26
    • 0027543961 scopus 로고
    • A nonsmooth version of Newton's method
    • L. Qi and J. Sun, A nonsmooth version of Newton's method, Math. Program., 58 (1993), pp. 353-367.
    • (1993) Math. Program. , vol.58 , pp. 353-367
    • Qi, L.1    Sun, J.2
  • 28
    • 0002125047 scopus 로고
    • Algorithms for solving equations
    • American Mathematical Society, Providence, RI
    • S. Smale, Algorithms for solving equations, in Proceedings of the International Congress of Mathematicians, American Mathematical Society, Providence, RI, 1987, pp. 172-195.
    • (1987) Proceedings of the International Congress of Mathematicians , pp. 172-195
    • Smale, S.1
  • 29
    • 0036474487 scopus 로고    scopus 로고
    • Semismooth matrix valued functions
    • D. Sun and J. Sun, Semismooth matrix valued functions, Math. Oper. Res., 27 (2002), pp. 150-169.
    • (2002) Math. Oper. Res. , vol.27 , pp. 150-169
    • Sun, D.1    Sun, J.2
  • 30
    • 60749092917 scopus 로고    scopus 로고
    • Löwner's operator and spectral functions on Euclidean Jordan algebras
    • D. Sun and J. Sun, Löwner's operator and spectral functions on Euclidean Jordan algebras, Math. Oper. Res., 33 (2008), pp. 421-445.
    • (2008) Math. Oper. Res. , vol.33 , pp. 421-445
    • Sun, D.1    Sun, J.2
  • 31
    • 21644437651 scopus 로고    scopus 로고
    • Strong semismoothness of the Fischer-Burmeister SDC and Soc complementarity functions
    • D. Sun and J. Sun, Strong semismoothness of the Fischer-Burmeister SDC and SOC complementarity functions, Math. Program., 103 (2005), pp. 575-582.
    • (2005) Math. Program. , vol.103 , pp. 575-582
    • Sun, D.1    Sun, J.2
  • 32
    • 4043052308 scopus 로고    scopus 로고
    • A squared smoothing Newton method for nonsmooth matrix equations and its applications in semidefinite optimization problems
    • J. Sun, D. Sun, and L. Qi, A squared smoothing Newton method for nonsmooth matrix equations and its applications in semidefinite optimization problems, SIAM J. Optim., 14 (2004), pp. 783-806.
    • (2004) SIAM. J. Optim. , vol.14 , pp. 783-806
    • Sun, J.1    Sun, D.2    Qi, L.3
  • 33
    • 31144435396 scopus 로고    scopus 로고
    • Some P-properties for nonlinear transformations on Euclidean Jordan algebras
    • J. Tao and M. S. Gowda, Some P-properties for nonlinear transformations on Euclidean Jordan algebras, Math. Oper. Res., 30 (2005), pp. 985-1004.
    • (2005) Math. Oper. Res. , vol.30 , pp. 985-1004
    • Tao, J.1    Gowda, M.S.2
  • 35
    • 24944552173 scopus 로고    scopus 로고
    • Computational Science and Its Applications-ICCSA 2005, Vol. 4, Proceedings Lecture Notes in Computer Science 3483, Springer, Berlin
    • Y. Xia and J. M. Peng, A continuation method for the linear second-order cone complementarity Problem, Computational Science and Its Applications-ICCSA 2005, Vol. 4, Proceedings Lecture Notes in Computer Science 3483, Springer, Berlin, 2005, pp. 290-300.
    • (2005) A Continuation Method for the Linear Second-Order Cone Complementarity Problem , pp. 290-300
    • Xia, Y.1    Peng, J.M.2
  • 36
    • 34547129415 scopus 로고    scopus 로고
    • On the level-boundedness of the natural residual function for variational inequality problems
    • N. Yamashita and M. Fukushima, On the level-boundedness of the natural residual function for variational inequality problems, Pac. J. Optim., 1 (2005), pp. 625-630.
    • (2005) Pac. J. Optim. , vol.1 , pp. 625-630
    • Yamashita, N.1    Fukushima, M.2
  • 37
    • 36248962181 scopus 로고    scopus 로고
    • Interior point trajectories and a homogeneous model for nonlinear complementarity problems over symmetric cones
    • A. Yoshise, Interior point trajectories and a homogeneous model for nonlinear complementarity problems over symmetric cones, SIAM J. Optim., 17 (2006), pp. 1129-1153.
    • (2006) SIAM. J. Optim. , vol.17 , pp. 1129-1153
    • Yoshise, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.