메뉴 건너뛰기




Volumn 23, Issue 1-2, 1998, Pages 45-51

Solving box constrained variational inequalities by using the natural residual with D-gap function globalization

Author keywords

D gap function; Finite termination; Global convergence; Mixed complementarity problem; Natural residual; Newton's method; Quadratic convergence; Variational inequality problem

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; NONLINEAR EQUATIONS; OPTIMIZATION; PROBLEM SOLVING; VARIATIONAL TECHNIQUES; VECTORS;

EID: 0032131672     PISSN: 01676377     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6377(98)00023-6     Document Type: Article
Times cited : (33)

References (19)
  • 1
    • 0023416451 scopus 로고
    • Projected gradient methods for linearly constrained problems
    • P.H. Calamai, J.J. Moré, Projected gradient methods for linearly constrained problems, Math. Programming 39 (1987) 93-116.
    • (1987) Math. Programming , vol.39 , pp. 93-116
    • Calamai, P.H.1    Moré, J.J.2
  • 2
    • 0041528074 scopus 로고    scopus 로고
    • A theoretical and numerical comparison of some semismooth algorithms for complementarity problems
    • Computer Sciences Department, University of Wisconsin, Madison, WI, December
    • T. De Luca, F. Facchinei, C. Kanzow, A theoretical and numerical comparison of some semismooth algorithms for complementarity problems, Mathematical Programming Technical Report 97-15, Computer Sciences Department, University of Wisconsin, Madison, WI, December 1997.
    • (1997) Mathematical Programming Technical Report 97-15
    • De Luca, T.1    Facchinei, F.2    Kanzow, C.3
  • 3
    • 0029423693 scopus 로고
    • The PATH solver: A non-monotone stabilization scheme for mixed complementarity problems
    • S.P. Dirkse, M.C. Ferris, The PATH solver: a non-monotone stabilization scheme for mixed complementarity problems, Optim. Methods Software 5 (1995) 123-156.
    • (1995) Optim. Methods Software , vol.5 , pp. 123-156
    • Dirkse, S.P.1    Ferris, M.C.2
  • 4
    • 0029425015 scopus 로고
    • MCPLIB: A collection of nonlinear mixed complementarity problems
    • S.P. Dirkse, M.C. Ferris, MCPLIB: a collection of nonlinear mixed complementarity problems, Optim. Methods Software 5 (1995) 319-345.
    • (1995) Optim. Methods Software , vol.5 , pp. 319-345
    • Dirkse, S.P.1    Ferris, M.C.2
  • 5
    • 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) 513-532.
    • (1997) Math. Programming , vol.76 , pp. 513-532
    • Fischer, A.1
  • 6
    • 0000310172 scopus 로고    scopus 로고
    • On finite termination of an iterative method for linear complementarity problems
    • A. Fischer, C. Kanzow, On finite termination of an iterative method for linear complementarity problems, Math. Programming 74 (1996) 279-292.
    • (1996) Math. Programming , vol.74 , pp. 279-292
    • Fischer, A.1    Kanzow, C.2
  • 7
    • 0026763569 scopus 로고
    • Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems
    • M. Fukushima, Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems, Math. Programming 53 (1992) 99-110.
    • (1992) Math. Programming , vol.53 , pp. 99-110
    • Fukushima, M.1
  • 8
    • 0002560226 scopus 로고    scopus 로고
    • Minimizing and stationary sequences of merit functions for complementarity problems and variational inequalities
    • M.C. Ferris, J.-S. Pang (Eds.), SIAM, Philadelphia, PA
    • M. Fukushima, J.-S. Pang, Minimizing and stationary sequences of merit functions for complementarity problems and variational inequalities, in: M.C. Ferris, J.-S. Pang (Eds.), Complementarity and Variational Problems: State of the Art, 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
  • 9
    • 0021522309 scopus 로고
    • Two-metric projection methods for constrained optimization
    • E.M. Gafni, D.P. Bertsekas, Two-metric projection methods for constrained optimization, SIAM. J. Control Optim. 22 (1984) 936-964.
    • (1984) SIAM. J. Control Optim. , vol.22 , pp. 936-964
    • Gafni, E.M.1    Bertsekas, D.P.2
  • 10
    • 0022766519 scopus 로고
    • A nonmonotone linesearch technique for Newton's method
    • L. Grippo, F. Lampariello, S. Lucidi, A nonmonotone linesearch technique for Newton's method, SIAM J. Numer. Anal. 23 (1986) 707-716.
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 707-716
    • Grippo, L.1    Lampariello, F.2    Lucidi, S.3
  • 12
    • 0002222760 scopus 로고    scopus 로고
    • Theoretical and numerical investigation of the D-gap function for box constrained variational inequalities
    • C. Kanzow, M. Fukushima, Theoretical and numerical investigation of the D-gap function for box constrained variational inequalities, Math. Programming, 83 (1998) 55-87.
    • (1998) Math. Programming , vol.83 , pp. 55-87
    • Kanzow, C.1    Fukushima, M.2
  • 13
    • 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) 959-972.
    • (1977) SIAM J. Control Optim. , vol.15 , pp. 959-972
    • Mifflin, R.1
  • 14
    • 0001070251 scopus 로고    scopus 로고
    • Equivalence of variational inequality problems to unconstrained optimization
    • J.-M. Peng, Equivalence of variational inequality problems to unconstrained optimization, Math. Programming 78 (1997) 347-356.
    • (1997) Math. Programming , vol.78 , pp. 347-356
    • Peng, J.-M.1
  • 16
    • 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) 227-244.
    • (1993) Math. Oper. Res. , vol.18 , pp. 227-244
    • Qi, L.1
  • 17
    • 0039069318 scopus 로고    scopus 로고
    • Regular pseudo-smooth NCP and BVIP functions and globally and quadratically convergent generalized Newton methods for complementarity and variational inequality problems
    • School of Mathematics, The University of New South Wales, Sydney, Australia, July (revised September 1997)
    • L. Qi, Regular pseudo-smooth NCP and BVIP functions and globally and quadratically convergent generalized Newton methods for complementarity and variational inequality problems, Applied Mathematics Report 97/14, School of Mathematics, The University of New South Wales, Sydney, Australia, July 1997 (revised September 1997).
    • (1997) Applied Mathematics Report 97/14
    • Qi, L.1
  • 18
    • 0001321899 scopus 로고    scopus 로고
    • A computable generalized Hessian of the D-gap function and Newton-type methods for variational inequality problems
    • M.C. Ferris, J.-S. Pang (Eds.), SIAM, Philadelphia, PA
    • D. Sun, M. Fukushima, L. Qi, A computable generalized Hessian of the D-gap function and Newton-type methods for variational inequality problems, in: M.C. Ferris, J.-S. Pang (Eds.), Complementarity and Variational Problems: State of the Art, SIAM, Philadelphia, PA, 1997, pp. 452-473.
    • (1997) Complementarity and Variational Problems: State of the Art , pp. 452-473
    • Sun, D.1    Fukushima, M.2    Qi, L.3
  • 19
    • 0031530152 scopus 로고    scopus 로고
    • Unconstrained optimization reformulations of variational inequality problems
    • N. Yamashita, K. Taji, M. Fukushima, Unconstrained optimization reformulations of variational inequality problems, J. Optim. Theory Appl. 92 (1997) 439-456.
    • (1997) J. Optim. Theory Appl. , vol.92 , pp. 439-456
    • Yamashita, N.1    Taji, K.2    Fukushima, M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.