메뉴 건너뛰기




Volumn 6, Issue 2, 1996, Pages 446-460

Equivalence of complementarity problems to differentiable minimization: A unified approach

Author keywords

Complementarity problem; Error bound; Merit function; Natural residual; Quadratic regularization

Indexed keywords


EID: 0030303845     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/0806024     Document Type: Article
Times cited : (39)

References (20)
  • 1
    • 0024739313 scopus 로고
    • Variational principles for variational inequalities
    • G. AUCHMUTY, Variational principles for variational inequalities, Numer. Funct. Anal. Optim., 10 (1989), pp. 863-874.
    • (1989) Numer. Funct. Anal. Optim. , vol.10 , pp. 863-874
    • Auchmuty, G.1
  • 4
    • 0003117688 scopus 로고
    • Implicit complementarity problems and quasi-variational inequalities
    • R. W. Cottle, F. Giannessi, and J.-L. Lions, eds., Wiley, New York
    • I. C. DOLCETTA AND U. MOSCO, Implicit complementarity problems and quasi-variational inequalities, in Variational Inequalities and Complementarity Problems: Theory and Applications, R. W. Cottle, F. Giannessi, and J.-L. Lions, eds., Wiley, New York, 1980, pp. 75-87.
    • (1980) Variational Inequalities and Complementarity Problems: Theory and Applications , pp. 75-87
    • Dolcetta, I.C.1    Mosco, U.2
  • 6
    • 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), pp. 99-110.
    • (1992) Math. Programming , vol.53 , pp. 99-110
    • Fukushima, M.1
  • 7
    • 0021522309 scopus 로고
    • Two-metric projection methods for constrained optimization
    • E. M. GAFNI AND D. P. BERTSEKAS, Two-metric projection methods for constrained optimization, SIAM J. Control Optim., 22 (1984), pp. 936-964.
    • (1984) SIAM J. Control Optim. , vol.22 , pp. 936-964
    • Gafni, E.M.1    Bertsekas, D.P.2
  • 8
    • 0030540616 scopus 로고    scopus 로고
    • Nonlinear complementarity as unconstrained optimization
    • to appear
    • C. KANZOW, Nonlinear complementarity as unconstrained optimization, J. Optim. Theory Appl., 88 (1996), to appear.
    • (1996) J. Optim. Theory Appl. , vol.88
    • Kanzow, C.1
  • 9
    • 0011352169 scopus 로고
    • On a global error bound for a class of monotone affine variational inequality problems
    • Z.-Q. LUO AND P. TSENG, On a global error bound for a class of monotone affine variational inequality problems, Oper. Res. Lett., 11 (1992), pp. 159-165.
    • (1992) Oper. Res. Lett. , vol.11 , pp. 159-165
    • Luo, Z.-Q.1    Tseng, P.2
  • 10
    • 21344480786 scopus 로고
    • Error bounds and convergence analysis of feasible descent methods: A general approach
    • _, Error bounds and convergence analysis of feasible descent methods: A general approach, Ann. Oper. Res., 46 (1993), pp. 157-178.
    • (1993) Ann. Oper. Res. , vol.46 , pp. 157-178
  • 11
    • 0000004762 scopus 로고
    • New error bounds for the linear complementarity problem
    • Z.-Q. LUO, O. L. MANGASARIAN, J. REN, AND M. V. SOLODOV, New error bounds for the linear complementarity problem, Math. Oper. Res., 19 (1994), pp. 880-892.
    • (1994) Math. Oper. Res. , vol.19 , pp. 880-892
    • Luo, Z.-Q.1    Mangasarian, O.L.2    Ren, J.3    Solodov, M.V.4
  • 12
    • 34249962654 scopus 로고
    • Error bounds for nondegenerate monotone linear complementarity problems
    • O. L. MANGASARIAN, Error bounds for nondegenerate monotone linear complementarity problems, Math. Programming, 48 (1990), pp. 437-445.
    • (1990) Math. Programming , vol.48 , pp. 437-445
    • Mangasarian, O.L.1
  • 13
    • 34250076671 scopus 로고
    • Nonlinear complementarity as unconstrained and constrained minimization
    • O. L. MANGASARIAN AND M. V. SOLODOV, Nonlinear complementarity as unconstrained and constrained minimization, Math. Programming, 62 (1993), pp. 277-297.
    • (1993) Math. Programming , vol.62 , pp. 277-297
    • Mangasarian, O.L.1    Solodov, M.V.2
  • 14
    • 38249017301 scopus 로고
    • Error bounds for the linear complementarity problem with a P-matrix
    • R. MATHIAS AND J.-S. PANG, Error bounds for the linear complementarity problem with a P-matrix, Linear Algebra Appl., 132 (1990), pp. 123-136.
    • (1990) Linear Algebra Appl. , vol.132 , pp. 123-136
    • Mathias, R.1    Pang, J.-S.2
  • 15
    • 0001491071 scopus 로고
    • Quasi-complementarity problem
    • M. A. NOOR, Quasi-complementarity problem, J. Math. Anal. Appl., 130 (1988), pp. 344-353.
    • (1988) J. Math. Anal. Appl. , vol.130 , pp. 344-353
    • Noor, M.A.1
  • 16
    • 0000804782 scopus 로고
    • The implicit complementarity problem
    • O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, eds., Academic Press, New York
    • J.-S. PANG, The implicit complementarity problem, in Nonlinear Programming 4, O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, eds., Academic Press, New York, 1981, pp. 487-518.
    • (1981) Nonlinear Programming , vol.4 , pp. 487-518
    • Pang, J.-S.1
  • 17
    • 0001170028 scopus 로고
    • A posteriori error bounds for the linearly-constrained variational inequality problem
    • _, A posteriori error bounds for the linearly-constrained variational inequality problem, Math. Oper. Res., 12 (1987), pp. 474-484.
    • (1987) Math. Oper. Res. , vol.12 , pp. 474-484
  • 18
    • 0003000071 scopus 로고
    • Complementarity problems
    • R. Horst and P. Pardalos, eds., Kluwer Academic Publishers, Norwell, MA
    • _, Complementarity problems, in Handbook on Global Optimization, R. Horst and P. Pardalos, eds., Kluwer Academic Publishers, Norwell, MA, 1995, pp. 271-338.
    • (1995) Handbook on Global Optimization , pp. 271-338
  • 19
    • 0027543289 scopus 로고
    • A globally convergent Newton method for solving strongly monotone variational inequalities
    • K. TAJI, M. FUKUSHIMA, AND T. IBARAKI, A globally convergent Newton method for solving strongly monotone variational inequalities, Math. Programming, 58 (1993), pp. 369-383.
    • (1993) Math. Programming , vol.58 , pp. 369-383
    • Taji, K.1    Fukushima, M.2    Ibaraki, T.3
  • 20
    • 21844488561 scopus 로고
    • On stationary points of the implicit Lagrangian for nonlinear complementarity problems
    • N. YAMASHITA AND M. FUKUSHIMA, On stationary points of the implicit Lagrangian for nonlinear complementarity problems, J. Optim. Theory Appl., 84 (1995), pp. 653-663.
    • (1995) J. Optim. Theory Appl. , vol.84 , pp. 653-663
    • Yamashita, N.1    Fukushima, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.