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Volumn 13, Issue 4, 2003, Pages 960-985

Analysis of nonsmooth symmetric-matrix-valued functions with applications to semidefinite complementarity problems

Author keywords

Nonsmooth analysis; Semidefinite complementarity problem; Semismooth function; Symmetric matrix valued function

Indexed keywords


EID: 0038485144     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623400380584     Document Type: Article
Times cited : (79)

References (32)
  • 1
    • 0004151496 scopus 로고    scopus 로고
    • Springer-Verlag, New York
    • R. BHATIA, Matrix Analysis, Springer-Verlag, New York, 1997.
    • (1997) Matrix Analysis
    • Bhatia, R.1
  • 2
    • 0039938688 scopus 로고    scopus 로고
    • 0 NCP or monotone NCP
    • 0 NCP or monotone NCP, SIAM J. Optim., 9 (1999), pp. 624-645.
    • (1999) SIAM J. Optim. , vol.9 , pp. 624-645
    • Chen, B.1    Chen, X.2
  • 3
    • 0031493118 scopus 로고    scopus 로고
    • Smoothing approximations to nonlinear complementarity problems
    • B. CHEN AND P.T. HARKER, Smoothing approximations to nonlinear complementarity problems, SIAM J. Optim., 7 (1997), pp. 403-420.
    • (1997) SIAM J. Optim. , vol.7 , pp. 403-420
    • Chen, B.1    Harker, P.T.2
  • 4
    • 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. Programming, 71 (1995), pp. 51-69.
    • (1995) Math. Programming , vol.71 , pp. 51-69
    • Chen, C.1    Mangasarian, O.L.2
  • 5
    • 0030104686 scopus 로고    scopus 로고
    • A class of smoothing functions for nonlinear and mixed complementarity problems
    • C. CHEN AND O.L. MANGASARIAN, A class of smoothing functions for nonlinear and mixed complementarity problems, Comput. Optim. Appl., 5 (1996), pp. 97-138.
    • (1996) Comput. Optim. Appl. , vol.5 , pp. 97-138
    • Chen, C.1    Mangasarian, O.L.2
  • 6
    • 0032380644 scopus 로고    scopus 로고
    • Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities
    • X. 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. Comp., 67 (1998), pp. 519-540.
    • (1998) Math. Comp. , vol.67 , pp. 519-540
    • Chen, X.1    Qi, L.2    Sun, D.3
  • 7
    • 0345148378 scopus 로고    scopus 로고
    • On homotopy-smoothing methods for box-constrained variational inequalities
    • X. CHEN AND Y. YE, On homotopy-smoothing methods for box-constrained variational inequalities, SIAM J. Control Optim., 37 (1999), pp. 589-616.
    • (1999) SIAM J. Control Optim. , vol.37 , pp. 589-616
    • Chen, X.1    Ye, Y.2
  • 8
    • 0009970144 scopus 로고    scopus 로고
    • Non-interior continuation methods for solving semidefinite complementarity problems
    • to appear
    • X. CHEN AND P. TSENG, Non-interior continuation methods for solving semidefinite complementarity problems, Math. Programming, to appear.
    • Math. Programming
    • Chen, X.1    Tseng, P.2
  • 10
    • 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), pp. 513-532.
    • (1997) Math. Programming , vol.76 , pp. 513-532
    • Fischer, A.1
  • 12
  • 14
    • 0012374684 scopus 로고    scopus 로고
    • Global and local superlinear convergence analysis of Newton-type methods for semismooth equations with smooth least squares
    • M. Fukushima and L. Qi, eds., Kluwer Academic Publishers, Boston
    • H. JIANG AND D. RALPH, Global and local superlinear convergence analysis of Newton-type methods for semismooth equations with smooth least squares, in Reformulation - Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, M. Fukushima and L. Qi, eds., Kluwer Academic Publishers, Boston, 1999, pp. 181-209.
    • (1999) Reformulation - Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods , pp. 181-209
    • Jiang, H.1    Ralph, D.2
  • 15
    • 0037289395 scopus 로고    scopus 로고
    • Semidefinite programs: New search directions, smoothing-type methods, and numerical results
    • C. KANZOW AND C. NAGEL, Semidefinite programs: New search directions, smoothing-type methods, and numerical results, SIAM J. Optim., 13 (2002), pp. 1-23.
    • (2002) SIAM J. Optim. , vol.13 , pp. 1-23
    • Kanzow, C.1    Nagel, C.2
  • 16
    • 0033418367 scopus 로고    scopus 로고
    • Jacobian smoothing methods for nonlinear complementarity problems
    • C. KANZOW AND H. PIEPER, Jacobian smoothing methods for nonlinear complementarity problems, SIAM J. Optim., 9 (1999), pp. 342-373.
    • (1999) SIAM J. Optim. , vol.9 , pp. 342-373
    • Kanzow, C.1    Pieper, H.2
  • 18
    • 0042602157 scopus 로고    scopus 로고
    • Eigenvalue optimization
    • A.S. LEWIS AND M.L. OVERTON, Eigenvalue optimization, Acta Numer., 5 (1996), pp. 149-190.
    • (1996) Acta Numer. , vol.5 , pp. 149-190
    • Lewis, A.S.1    Overton, M.L.2
  • 19
    • 0036057564 scopus 로고    scopus 로고
    • Twice differentiable spectral functions
    • A.S. LEWIS AND H.S. SENDOV, Twice differentiable spectral functions, SIAM J. Matrix Anal. Appl., 23 (2001), pp. 368-386.
    • (2001) SIAM J. Matrix Anal. Appl. , vol.23 , pp. 368-386
    • Lewis, A.S.1    Sendov, H.S.2
  • 20
    • 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), pp. 959-972.
    • (1977) SIAM J. Control Optim. , vol.15 , pp. 959-972
    • Mifflin, R.1
  • 21
    • 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), pp. 227-244.
    • (1993) Math. Oper. Res. , vol.18 , pp. 227-244
    • Qi, L.1
  • 22
    • 0007546250 scopus 로고    scopus 로고
    • 0-functions
    • 0-functions, SIAM J. Optim., 10 (1999), pp. 315-330.
    • (1999) SIAM J. Optim. , vol.10 , pp. 315-330
    • Qi, H.-D.1
  • 23
    • 0027543961 scopus 로고
    • A nonsmooth version of Newton's method
    • L. QI AND J. SUN, A nonsmooth version of Newton's method, Math. Programming, 58 (1993), pp. 353-367.
    • (1993) Math. Programming , vol.58 , pp. 353-367
    • Qi, L.1    Sun, J.2
  • 24
    • 0002287357 scopus 로고    scopus 로고
    • A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities
    • L. QI, D. SUN, AND G. ZHOU, A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities, Math. Programming, 87 (2000), pp. 1-35.
    • (2000) Math. Programming , vol.87 , pp. 1-35
    • Qi, L.1    Sun, D.2    Zhou, G.3
  • 27
    • 0242671725 scopus 로고    scopus 로고
    • Monotone Semidefinite Complementarity Problems
    • Department of Mathematical and Computer Sciences, Tokyo Institute of Technology, Tokyo
    • M. SHIDA AND S. SHINDOH, Monotone Semidefinite Complementarity Problems, Research Report 312, Department of Mathematical and Computer Sciences, Tokyo Institute of Technology, Tokyo, 1996.
    • (1996) Research Report , vol.312
    • Shida, M.1    Shindoh, S.2
  • 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
    • 0000882736 scopus 로고    scopus 로고
    • Merit functions for semi-definite complementarity problems
    • P. TSENG, Merit functions for semi-definite complementarity problems, Math. Programming, 83 (1998), pp. 159-185.
    • (1998) Math. Programming , vol.83 , pp. 159-185
    • Tseng, P.1
  • 31
    • 0000697391 scopus 로고    scopus 로고
    • Analysis of a non-interior continuation method based on Chen-Mangasarian smoothing functions for complementarity problems
    • M. Fukushima and L. Qi, eds., Kluwer Academic Publishers, Boston
    • P. TSENG, Analysis of a non-interior continuation method based on Chen-Mangasarian smoothing functions for complementarity problems, in Reformulation-Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, M. Fukushima and L. Qi, eds., Kluwer Academic Publishers, Boston, 1999, pp. 381-404.
    • (1999) Reformulation-Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods , pp. 381-404
    • Tseng, P.1
  • 32
    • 0013468266 scopus 로고    scopus 로고
    • A new merit function and a descent method for semidefinite complementarity problems
    • M. Fukushima and L. Qi, eds., Kluwer Academic Publishers, Boston
    • N. YAMASHITA AND M. FUKUSHIMA, A new merit function and a descent method for semidefinite complementarity problems, in Reformulation - Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, M. Fukushima and L. Qi, eds., Kluwer Academic Publishers, Boston, 1999, pp. 405-420.
    • (1999) Reformulation - Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods , pp. 405-420
    • Yamashita, N.1    Fukushima, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.