메뉴 건너뛰기




Volumn 35, Issue 2, 2006, Pages 199-237

A smoothing newton-type algorithm of stronger convergence for the quadratically constrained convex quadratic programming

Author keywords

Global convergence; Smoothing Newton method; Superlinear convergence

Indexed keywords

GLOBAL CONVERGENCE; SMOOTHING NEWTON METHOD; SUPERLINEAR CONVERGENCE;

EID: 33749614928     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-006-6512-7     Document Type: Article
Times cited : (38)

References (41)
  • 5
    • 0036002580 scopus 로고    scopus 로고
    • Improved smoothing-type methods for the solution of linear programming
    • S. Engelke and C. Kanzow, "Improved smoothing-type methods for the solution of linear programming," Numer. Math., vol. 90, pp. 487-507, 2002.
    • (2002) Numer. Math. , vol.90 , pp. 487-507
    • Engelke, S.1    Kanzow, C.2
  • 6
    • 0032244001 scopus 로고    scopus 로고
    • On the accurate identification of active constrains
    • F. Facchnei, A. Fischer, and C. Kanzow, "On the accurate identification of active constrains," SIAM J. Optim., vol. 9, pp. 14-32, 1998.
    • (1998) SIAM J. Optim. , vol.9 , pp. 14-32
    • Facchnei, F.1    Fischer, A.2    Kanzow, C.3
  • 7
    • 0032657647 scopus 로고    scopus 로고
    • Beyond monotonicity in regularization methods for nonlinear complementarity problems
    • F. Facchnei and C. Kanzow, "Beyond monotonicity in regularization methods for nonlinear complementarity problems," SIAM J. Control Optim., vol. 37, pp. 1150-1161, 1999.
    • (1999) SIAM J. Control Optim. , vol.37 , pp. 1150-1161
    • Facchnei, F.1    Kanzow, C.2
  • 9
    • 0000554369 scopus 로고    scopus 로고
    • Solution of monotone complementarity problems with Lipschitzian functions
    • A. Fischer, "Solution of monotone complementarity problems with Lipschitzian functions," Math. Program., vol. 76, pp. 513-532, 1997.
    • (1997) Math. Program. , vol.76 , pp. 513-532
    • Fischer, A.1
  • 10
    • 14944383664 scopus 로고    scopus 로고
    • Local beharior of an iterative framework for generalized equations with nonisolated solutions
    • A. Fischer, "Local beharior of an iterative framework for generalized equations with nonisolated solutions," Math. Program., vol. 94, pp. 91-124, 2002.
    • (2002) Math. Program. , vol.94 , pp. 91-124
    • Fischer, A.1
  • 11
    • 0033077146 scopus 로고    scopus 로고
    • Weak univalence and connectedness of inverse images of continuous functions
    • M.S. Gowda and J.J. Sznajder, "Weak univalence and connectedness of inverse images of continuous functions," Math. Oper. Res., vol. 24, pp. 255-261, 1999.
    • (1999) Math. Oper. Res. , vol.24 , pp. 255-261
    • Gowda, M.S.1    Sznajder, J.J.2
  • 12
    • 0036600646 scopus 로고    scopus 로고
    • 0 function nonlinear complementarity problem
    • 0 function nonlinear complementarity problem," Oper. Res. Letters, vol. 30, pp. 202-210, 2002.
    • (2002) Oper. Res. Letters , vol.30 , pp. 202-210
    • Huang, Z.H.1
  • 15
    • 0016941970 scopus 로고
    • Complementarity problems over cones with monotone and pseudomonotone maps
    • S. Karamardian, "Complementarity problems over cones with monotone and pseudomonotone maps," J. Optim. Theory Appl., vol. 18, pp. 445-454, 1976.
    • (1976) J. Optim. Theory Appl. , vol.18 , pp. 445-454
    • Karamardian, S.1
  • 16
    • 0002416157 scopus 로고
    • Strongly stable stationary solutions in nonlinear programs
    • S.M. Robinson (ed.), Academic Press, New York
    • M. Kojima, "Strongly stable stationary solutions in nonlinear programs," in S.M. Robinson (ed.), Analysis and Computation of Fixed Points, Academic Press, New York, pp. 93-138, 1980.
    • (1980) Analysis and Computation of Fixed Points , pp. 93-138
    • Kojima, M.1
  • 18
    • 0000159204 scopus 로고
    • Stable monotone variational inequalities
    • L. Mclinden, "Stable monotone variational inequalities," Math. Program., vol. 48, pp. 303-338, 1990.
    • (1990) Math. Program. , vol.48 , pp. 303-338
    • Mclinden, L.1
  • 19
    • 0000012763 scopus 로고
    • Semismooth and semiconvex functions in constrained optimization
    • R. Mifflin, " Semismooth and semiconvex functions in constrained optimization," SIAM J. Control Optim., vol. 15, pp. 957-972, 1977.
    • (1977) SIAM J. Control Optim. , vol.15 , pp. 957-972
    • Mifflin, R.1
  • 20
    • 0030134078 scopus 로고    scopus 로고
    • A superlinearly convergent infeasible-interior-point algorithm for geometrical LCPs without strictly complementary condition
    • S. Mizuno, "A superlinearly convergent infeasible-interior-point algorithm for geometrical LCPs without strictly complementary condition," Math. Oper. Res., vol. 21, pp. 382-400, 1996.
    • (1996) Math. Oper. Res. , vol.21 , pp. 382-400
    • Mizuno, S.1
  • 23
    • 0035602811 scopus 로고    scopus 로고
    • Second-order algorithm for generalized finite and semi-infinite min-max problems
    • E. Polak, L. Qi, and D. Sun, "Second-order algorithm for generalized finite and semi-infinite min-max problems," SIAM J. Optim., vol. 11, pp. 937-961, 2001.
    • (2001) SIAM J. Optim. , vol.11 , pp. 937-961
    • Polak, E.1    Qi, L.2    Sun, D.3
  • 24
    • 0007546250 scopus 로고    scopus 로고
    • A regularized smoothing Newton method for box constrained variational inequality problems with Po-functions
    • H.D. Qi, "A regularized smoothing Newton method for box constrained variational inequality problems with Po-functions," SIAM J. Optim., vol. 10, pp. 315-330, 2000.
    • (2000) SIAM J. Optim. , vol.10 , pp. 315-330
    • Qi, H.D.1
  • 25
    • 0027543961 scopus 로고
    • A nonsmooth version of Newton's method
    • L. Qi and J. Sun, "A nonsmooth version of Newton's method," Math. Program., vol. 58, pp. 353-367, 1993.
    • (1993) Math. Program. , vol.58 , pp. 353-367
    • Qi, L.1    Sun, J.2
  • 26
    • 0002287357 scopus 로고    scopus 로고
    • A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequality problems
    • L. Qi, D. Sun, and G. Zhou, "A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequality problems," Math. Program., vol. 87, pp. 1-35, 2000.
    • (2000) Math. Program. , vol.87 , pp. 1-35
    • Qi, L.1    Sun, D.2    Zhou, G.3
  • 27
    • 0002893535 scopus 로고    scopus 로고
    • Superlinear convergence of an interior point method for monotone variational inequalities
    • SIAM
    • D. Ralph and S.J. Wright, "Superlinear convergence of an interior point method for monotone variational inequalities," Complementarity and Variational Problems: State of the Art, SIAM, pp. 345-385, 1997.
    • (1997) Complementarity and Variational Problems: State of the Art , pp. 345-385
    • Ralph, D.1    Wright, S.J.2
  • 28
    • 0034187335 scopus 로고    scopus 로고
    • Superlinear convergence of an interior point method despite dependent constraints
    • D. Ralph and S.J. Wright, "Superlinear convergence of an interior point method despite dependent constraints," Math. Oper. Res., vol. 25, pp. 179-194, 2000.
    • (2000) Math. Oper. Res. , vol.25 , pp. 179-194
    • Ralph, D.1    Wright, S.J.2
  • 29
    • 0035238733 scopus 로고    scopus 로고
    • 0-functions in box variational inequality problems
    • 0-functions in box variational inequality problems," SIAM J. Optim., vol. 11, pp. 748-760, 2001.
    • (2001) SIAM J. Optim. , vol.11 , pp. 748-760
    • Ravindran, G.1    Gowda, M.S.2
  • 30
    • 0001272077 scopus 로고
    • Normal maps induced by linear transformation
    • S.M. Robinson, "Normal maps induced by linear transformation," Math. Oper. Res., vol. 17, pp. 691-714, 1992.
    • (1992) Math. Oper. Res. , vol.17 , pp. 691-714
    • Robinson, S.M.1
  • 31
    • 0032207259 scopus 로고    scopus 로고
    • Hight order infeasible-interior-point methods for solving sufficient linear complementarity problems
    • J. Stoer, M. Weches, and S. Mizuno, "Hight order infeasible-interior-point methods for solving sufficient linear complementarity problems," Math. Oper. Res., vol. 23, pp. 832-862, 1998.
    • (1998) Math. Oper. Res. , vol.23 , pp. 832-862
    • Stoer, J.1    Weches, M.2    Mizuno, S.3
  • 32
    • 0033077428 scopus 로고    scopus 로고
    • Superlinear convergence of an algorithm for monotone linear complementarity problems, when no strictly complementary solution exists
    • J.F. Sturm, "Superlinear convergence of an algorithm for monotone linear complementarity problems, when no strictly complementary solution exists," Math. Oper. Res., vol. 24, pp. 72-94, 1999.
    • (1999) Math. Oper. Res. , vol.24 , pp. 72-94
    • Sturm, J.F.1
  • 33
    • 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., vol. 36, pp. 315-339, 1999.
    • (1999) Appl. Math. Optim. , vol.36 , pp. 315-339
    • Sun, D.1
  • 34
    • 0032390326 scopus 로고    scopus 로고
    • Quadratic convergence of a long-step interior point method for nonlinear monotone variational inequality problems
    • J. Sun and G. Zhao, "Quadratic convergence of a long-step interior point method for nonlinear monotone variational inequality problems," J. Optim. Theory Appl., vol. 97, pp. 471-491, 1998.
    • (1998) J. Optim. Theory Appl. , vol.97 , pp. 471-491
    • Sun, J.1    Zhao, G.2
  • 35
    • 0002621771 scopus 로고    scopus 로고
    • Error bounds and superlinear convergence analysis of some Newton-type methods in optimization
    • Di G. Pillo and F. Oiannessi (eds.), Kluwer Academic Publishers, Boston
    • P. Tseng, "Error bounds and superlinear convergence analysis of some Newton-type methods in optimization," in Nonlinear Optimization and Related Topics, Di G. Pillo and F. Oiannessi (eds.), Kluwer Academic Publishers, Boston, pp. 445-462, 2000.
    • (2000) Nonlinear Optimization and Related Topics , pp. 445-462
    • Tseng, P.1
  • 37
    • 0011662308 scopus 로고    scopus 로고
    • On the rate of convergence of the Levenberg-Marquardt method
    • N. Yamashita and M. Fukushima, "On the rate of convergence of the Levenberg-Marquardt method," Computing[Suppl], vol. 15, pp. 239-249, 2001.
    • (2001) Computing[Suppl] , vol.15 , pp. 239-249
    • Yamashita, N.1    Fukushima, M.2
  • 38
    • 0027803251 scopus 로고
    • On quadratic and O(√nL) convergence of a predictor-corrector algorithm for LCP
    • Y. Ye and K. Anstreicher, "On quadratic and O(√nL) convergence of a predictor-corrector algorithm for LCP," Math. Program., vol. 62, pp. 537-552, 1993.
    • (1993) Math. Program. , vol.62 , pp. 537-552
    • Ye, Y.1    Anstreicher, K.2
  • 39
    • 0027576307 scopus 로고
    • A quadratically convergent O(√nL)-iteration algorithm for linear programming
    • Y. Ye, O. Güler, R.A. Tapia, and Y. Zhang, "A quadratically convergent O(√nL)-iteration algorithm for linear programming," Math. Program., vol. 59, pp. 151-162, 1993.
    • (1993) Math. Program. , vol.59 , pp. 151-162
    • Ye, Y.1    Güler, O.2    Tapia, R.A.3    Zhang, Y.4
  • 40
    • 0000195638 scopus 로고
    • On superlinear and quadratic convergence of primal-dual interior point linear programming algorithms
    • Y. Zhang, R.A. Tapia, and J.E. Dennis, "On superlinear and quadratic convergence of primal-dual interior point linear programming algorithms." SIAM J. Optim., vol. 2, pp. 304-324, 1992.
    • (1992) SIAM J. Optim. , vol.2 , pp. 304-324
    • Zhang, Y.1    Tapia, R.A.2    Dennis, J.E.3
  • 41
    • 0032595831 scopus 로고    scopus 로고
    • On the rate of local convergence of high-order infeasible-path-following algorithms for P*-LCP with or without strictly complementary solutions
    • G. Zhao and J. Sun, "On the rate of local convergence of high-order infeasible-path-following algorithms for P*-LCP with or without strictly complementary solutions," Comput. Optim. Appl., vol. 14, pp. 293-307, 1999.
    • (1999) Comput. Optim. Appl. , vol.14 , pp. 293-307
    • Zhao, G.1    Sun, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.