메뉴 건너뛰기




Volumn 73, Issue 3, 1996, Pages 251-268

Generalized equations and the generalized Newton method

Author keywords

Generalized equations; Generalized newton method; Kantorovich theorem; Mentarity problem; Nonlinear comple; Variational inequalities

Indexed keywords


EID: 28044444940     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02592214     Document Type: Article
Times cited : (28)

References (39)
  • 5
    • 34250511959 scopus 로고
    • Nonlinear maximal monotone operators in Banach spaces
    • F.E. Browder "Nonlinear maximal monotone operators in Banach spaces," Mathematische Annalen 176 (1968) 88-113.
    • (1968) Mathematische Annalen , vol.176 , pp. 88-113
    • Browder, F.E.1
  • 7
    • 34250257862 scopus 로고
    • Auxilliary problem principle and decomposition of optimization problems
    • G. Cohen, "Auxilliary problem principle and decomposition of optimization problems," Journal of Optimization Theory and Applications 32 (1980) 277-305.
    • (1980) Journal of Optimization Theory and Applications , vol.32 , pp. 277-305
    • Cohen, G.1
  • 9
    • 0015111628 scopus 로고
    • The solution of a quadratic programming problem using systematic overrelaxation
    • C.W. Cryer, "The solution of a quadratic programming problem using systematic overrelaxation," SIAM Journal on Control 9 (1971) 385-392.
    • (1971) SIAM Journal on Control , vol.9 , pp. 385-392
    • Cryer, C.W.1
  • 13
    • 0344704362 scopus 로고
    • Finite dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications
    • P.T. Harker and J.S. Pang, "Finite dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications," Mathematical Programming 48 (1990) 161-220.
    • (1990) Mathematical Programming , vol.48 , pp. 161-220
    • Harker, P.T.1    Pang, J.S.2
  • 14
    • 0027110831 scopus 로고
    • Local convergence of quasi-Newton methods for B-differentiable equations
    • C.M. Ip and J. Kyparisis, "Local convergence of quasi-Newton methods for B-differentiable equations," Mathematical Programming 56 (1992) 71-90.
    • (1992) Mathematical Programming , vol.56 , pp. 71-90
    • Ip, C.M.1    Kyparisis, J.2
  • 15
    • 0004219579 scopus 로고
    • Newton's method for generalized equations
    • Mathematics Research Center, University of Wisconsin Madison, WI
    • N.H. Josephy, "Newton's method for generalized equations," Technical Report No. 1965, Mathematics Research Center, University of Wisconsin (Madison, WI, 1979).
    • (1979) Technical Report No. 1965
    • Josephy, N.H.1
  • 16
    • 0004219579 scopus 로고
    • A newton method for the PIES energy model
    • Mathematics Research Center, University of Wisconsin Madison, WI
    • N.H. Josephy, "A Newton method for the PIES energy model," Technical Report No. 1977, Mathematics Research Center, University of Wisconsin (Madison, WI, 1979).
    • (1979) Technical Report No. 1977
    • Josephy, N.H.1
  • 21
    • 34247595796 scopus 로고
    • Solution of symmetric linear complementarity problems by iterative methods
    • O.L. Mangasarian, "Solution of symmetric linear complementarity problems by iterative methods," Journal of Optimization Theory and Applications 22 (1977) 465-485.
    • (1977) Journal of Optimization Theory and Applications , vol.22 , pp. 465-485
    • Mangasarian, O.L.1
  • 22
    • 84972544360 scopus 로고
    • On the monotonicity of the gradient of a convex function
    • G.J. Minty, "On the monotonicity of the gradient of a convex function," Pacific Journal of Mathematics 14 (1964) 243-247.
    • (1964) Pacific Journal of Mathematics , vol.14 , pp. 243-247
    • Minty, G.J.1
  • 23
    • 84972488065 scopus 로고
    • Monotone (nonlinear) operators in Hilbert space
    • G.J. Minty, "Monotone (nonlinear) operators in Hilbert space," Duke Mathematics Journal 29 (1973) 341-346.
    • (1973) Duke Mathematics Journal , vol.29 , pp. 341-346
    • Minty, G.J.1
  • 27
    • 0001601094 scopus 로고
    • Newton's method for B-differentiable equations
    • J.S. Pang, "Newton's method for B-differentiable equations," Mathematics of Operations Research 15 (1990) 311-341.
    • (1990) Mathematics of Operations Research , vol.15 , pp. 311-341
    • Pang, J.S.1
  • 28
    • 0020243016 scopus 로고
    • Iterative methods for variational and complementarity problems
    • J.S. Pang and D. Chan, "Iterative methods for variational and complementarity problems," Mathematical Programming 24 (1982) 284-313.
    • (1982) Mathematical Programming , vol.24 , pp. 284-313
    • Pang, J.S.1    Chan, D.2
  • 29
    • 0003317924 scopus 로고
    • Nonsmooth equations: Motivations and algorithms
    • J.S. Pang and L. Qi, "Nonsmooth equations: motivations and algorithms," SIAM Journal on Optimization 3 (1993) 443-465.
    • (1993) SIAM Journal on Optimization , vol.3 , pp. 443-465
    • Pang, J.S.1    Qi, L.2
  • 30
    • 0000607524 scopus 로고
    • Convergence analysis of some algorithms for solving non-smooth equations
    • L. Qi, "Convergence analysis of some algorithms for solving non-smooth equations," Mathematics of Operations Research 18 (1993) 227-244.
    • (1993) Mathematics of Operations Research , vol.18 , pp. 227-244
    • Qi, L.1
  • 31
    • 0000056025 scopus 로고
    • Generalized equations and their solutions, part I: Basic theory
    • S.M. Robinson, "Generalized equations and their solutions, part I: basic theory," Mathematical Programming Study 10 (1979) 128-141.
    • (1979) Mathematical Programming Study , vol.10 , pp. 128-141
    • Robinson, S.M.1
  • 33
    • 0002939936 scopus 로고
    • Generalized equations
    • A. Bachem, M. Grëtschel and B. Korte, eds., Springer, Berlin
    • S.M. Robinson, "Generalized equations," in: A. Bachem, M. Grëtschel and B. Korte, eds., Mathematical Programming: the State of the Art (Springer, Berlin, 1982) pp. 346-367.
    • (1982) Mathematical Programming: the State of the Art , pp. 346-367
    • Robinson, S.M.1
  • 35
    • 0000816132 scopus 로고
    • The Kantorovich Theorem for Newton's method
    • R.A. Tapia, "The Kantorovich Theorem for Newton's method," American Mathematical Monthly 78 (1971) 389-392.
    • (1971) American Mathematical Monthly , vol.78 , pp. 389-392
    • Tapia, R.A.1
  • 36
    • 0039090461 scopus 로고
    • The solution of finite dimensional variational inequalities using systematic relaxation
    • L.U. Uko, "The solution of finite dimensional variational inequalities using systematic relaxation," Journal of the Nigerian Mathematical Society 8 (1989) 61-75.
    • (1989) Journal of the Nigerian Mathematical Society , vol.8 , pp. 61-75
    • Uko, L.U.1
  • 38
    • 0039090460 scopus 로고
    • On a class of general strongly nonlinear quasivariational inequalities
    • L.U. Uko, "On a class of general strongly nonlinear quasivariational inequalities," Rivista di Matematica Pura ed Applicata 11 (1992) 47-55.
    • (1992) Rivista di Matematica Pura Ed Applicata , vol.11 , pp. 47-55
    • Uko, L.U.1
  • 39
    • 0027911171 scopus 로고
    • Remarks on the generalized Newton method
    • L.U. Uko, "Remarks on the generalized Newton method," Mathematical Programming 59 (1993) 405-412.
    • (1993) Mathematical Programming , vol.59 , pp. 405-412
    • Uko, L.U.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.