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Volumn 52, Issue 11, 2009, Pages 2341-2361

On filter-successive linearization methods for nonlinear semidefinite programming

Author keywords

Filter method; Global convergence; Nonlinear optimization; Semidefinite programming; Successive linearization method

Indexed keywords


EID: 71249096395     PISSN: 10069283     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11425-009-0168-6     Document Type: Article
Times cited : (30)

References (38)
  • 1
    • 0000920501 scopus 로고    scopus 로고
    • Semidefinite optimization
    • Todd M J. Semidefinite optimization. Acta Numer, 10: 515-560 (2001).
    • (2001) Acta Numer , vol.10 , pp. 515-560
    • Todd, M.J.1
  • 2
    • 0030106462 scopus 로고    scopus 로고
    • Semidefinite programming
    • Vandenberghe L, Boyd S. Semidefinite programming. SIAM Review, 38: 49-95 (1996).
    • (1996) SIAM Review , vol.38 , pp. 49-95
    • Vandenberghe, L.1    Boyd, S.2
  • 3
    • 0003395487 scopus 로고    scopus 로고
    • H. Wolkowicz, R. Saigal, and L. Vandenberghe (Eds.), Boston-Dordrecht-London: Kluwer Academic Publishers
    • Wolkowicz H, Saigal R, Vandenberghe L, eds. Handbook of Semidefinite Programming. Boston-Dordrecht-London: Kluwer Academic Publishers, 2000.
    • (2000) Handbook of Semidefinite Programming
  • 4
    • 0005740806 scopus 로고    scopus 로고
    • Semidefinite programming for combinatorial optimization
    • Helmberg C. Semidefinite programming for combinatorial optimization. Semidefinite programming home page: http://www.zib.de/helmberg/semidef.html (2000).
    • (2000) Semidefinite programming home page
    • Helmberg, C.1
  • 5
    • 14944366899 scopus 로고    scopus 로고
    • A global algorithm for nonlinear semidefinite programming
    • Correa R, Ramirez H. A global algorithm for nonlinear semidefinite programming. SIAM J Optim, 15: 303-318 (2004).
    • (2004) SIAM J Optim , vol.15 , pp. 303-318
    • Correa, R.1    Ramirez, H.2
  • 6
    • 0345817719 scopus 로고    scopus 로고
    • An interior method for nonconvex semidefinite programs
    • Jerre F. An interior method for nonconvex semidefinite programs. Optim Eng, 1: 347-372 (2000).
    • (2000) Optim Eng , vol.1 , pp. 347-372
    • Jerre, F.1
  • 7
    • 23944460017 scopus 로고    scopus 로고
    • Successive linearization methods for nonlinear semidefinite programs
    • Kanzow C, Nagel C, Kato H, et al. Successive linearization methods for nonlinear semidefinite programs. Comput Optim Appl, 31: 251-273 (2005).
    • (2005) Comput Optim Appl , vol.31 , pp. 251-273
    • Kanzow, C.1    Nagel, C.2    Kato, H.3
  • 8
    • 41149143510 scopus 로고    scopus 로고
    • The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming
    • Sun D, Sun J, Zhang L. The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming. Math Program, 114: 349-391 (2008).
    • (2008) Math Program , vol.114 , pp. 349-391
    • Sun, D.1    Sun, J.2    Zhang, L.3
  • 9
    • 4043052308 scopus 로고    scopus 로고
    • A squared smoothing Newton method for nonsmooth matrix equations and its applications in semidefinite optimization problems
    • Sun J, Sun D, Qi L. A squared smoothing Newton method for nonsmooth matrix equations and its applications in semidefinite optimization problems. SIAM J Optim, 14: 783-806 (2004).
    • (2004) SIAM J Optim , vol.14 , pp. 783-806
    • Sun, J.1    Sun, D.2    Qi, L.3
  • 10
    • 71249122994 scopus 로고    scopus 로고
    • Some properties for nonconvex semidefinite programming
    • Li C, Sun W. Some properties for nonconvex semidefinite programming. Numer Math J Chinese Univ, 30: 184-192 (2008).
    • (2008) Numer Math J Chinese Univ , vol.30 , pp. 184-192
    • Li, C.1    Sun, W.2
  • 11
    • 71249143342 scopus 로고    scopus 로고
    • A class of nonsmooth Newton-type methods for nonlinear semidefinite programming
    • Li C, Sun W. A class of nonsmooth Newton-type methods for nonlinear semidefinite programming. J Nanjing Norm Univ Nat Sci Ed, 31: 1-7 (2008).
    • (2008) J Nanjing Norm Univ Nat Sci Ed , vol.31 , pp. 1-7
    • Li, C.1    Sun, W.2
  • 12
    • 71249133914 scopus 로고    scopus 로고
    • A filter-sequential semidefinite programming method for nonlinear semidefinite programming
    • Nanjing Normal University
    • Li C, Sun W. A filter-sequential semidefinite programming method for nonlinear semidefinite programming. Technical Report Opt-07-03, School of Mathematics and Computer Science, Nanjing Normal University, 2007.
    • (2007) Technical Report Opt-07-03, School of Mathematics and Computer Science
    • Li, C.1    Sun, W.2
  • 13
    • 0042640552 scopus 로고    scopus 로고
    • A potential reduction algorithm for an extended SDP problem
    • Nie J, Yuan Y. A potential reduction algorithm for an extended SDP problem. Sci China Ser A, 43: 35-46 (2000).
    • (2000) Sci China Ser A , vol.43 , pp. 35-46
    • Nie, J.1    Yuan, Y.2
  • 15
    • 71249135422 scopus 로고    scopus 로고
    • Filter primal-dual interior point method for nonlinear semidefinite programming
    • Nanjing Normal University
    • Liu Z, Sun W. A filter primal-dual interior point method for nonlinear semidefinite programming. Technique report, School of Mathematics and Computer Science, Nanjing Normal University, 2008.
    • (2008) Technique Report, School of Mathematics and Computer Science
    • Liu, Z.1    Sun, W.2
  • 16
    • 0031139858 scopus 로고    scopus 로고
    • First and second order analysis of nonlinear semidefinite programs
    • Shapiro A. First and second order analysis of nonlinear semidefinite programs. Math Program, 77: 301-320 (1997).
    • (1997) Math Program , vol.77 , pp. 301-320
    • Shapiro, A.1
  • 17
    • 33746089809 scopus 로고    scopus 로고
    • The strong second order sufficient condition and constraint nondegeneracy in nonlinear semidefinite programming and their implications
    • Sun D. The strong second order sufficient condition and constraint nondegeneracy in nonlinear semidefinite programming and their implications. Math Oper Res, 31: 761-776 (2006).
    • (2006) Math Oper Res , vol.31 , pp. 761-776
    • Sun, D.1
  • 19
    • 0032208079 scopus 로고    scopus 로고
    • Sensitivity analysis of optimization problem under second order regularity constraints
    • Bonnans J F, Commintti R, Shapiro A. Sensitivity analysis of optimization problem under second order regularity constraints. Math Oper Res, 23: 803-832 (1998).
    • (1998) Math Oper Res , vol.23 , pp. 803-832
    • Bonnans, J.F.1    Commintti, R.2    Shapiro, A.3
  • 20
    • 35448933276 scopus 로고    scopus 로고
    • Approximation bounds for quadratic maximization and max-cut problems with semidefinite programming relaxation
    • Xu D C, Xu S Z. Approximation bounds for quadratic maximization and max-cut problems with semidefinite programming relaxation. Sci China Ser A, 50: 1583-1596 (2007).
    • (2007) Sci China Ser A , vol.50 , pp. 1583-1596
    • Xu, D.C.1    Xu, S.Z.2
  • 21
    • 0001556338 scopus 로고    scopus 로고
    • Nonlinear programming without a penalty function
    • Fletcher R, Leyffer S. Nonlinear programming without a penalty function. Math Program, 91: 239-269 (2002).
    • (2002) Math Program , vol.91 , pp. 239-269
    • Fletcher, R.1    Leyffer, S.2
  • 22
    • 0042354662 scopus 로고    scopus 로고
    • Global convergence of a trust-region SQP-filter algorithm for general nonlinear programming
    • Fletcher R, Gould N I M, Leyffer S, et al. Global convergence of a trust-region SQP-filter algorithm for general nonlinear programming. SIAM J Optim, 13: 635-659 (2002).
    • (2002) SIAM J Optim , vol.13 , pp. 635-659
    • Fletcher, R.1    Gould, N.I.M.2    Leyffer, S.3
  • 23
    • 0013468012 scopus 로고    scopus 로고
    • On the global convergence of an SLP-filter algorithm
    • Scotland: Department of Mathematics, University of Dundee
    • Fletcher R, Leyffer S, Toint Ph L. On the global convergence of an SLP-filter algorithm. Numerical Analysis Report NA/183, Department of Mathematics, University of Dundee, Scotland, 1998.
    • (1998) Numerical Analysis Report NA/183
    • Fletcher, R.1    Leyffer, S.2    Toint, P.L.3
  • 24
    • 0037288670 scopus 로고    scopus 로고
    • On the global convergence of a filter-SQP algorithm
    • Fletcher R, Leyffer S, Toint Ph L. On the global convergence of a filter-SQP algorithm. SIAM J Optim, 13: 44-59 (2002).
    • (2002) SIAM J Optim , vol.13 , pp. 44-59
    • Fletcher, R.1    Leyffer, S.2    Toint, P.L.3
  • 25
    • 33646721213 scopus 로고    scopus 로고
    • A filter-trust-region method for unconstrained optimization
    • Gould N I M, Sainvitu C, Toint Ph L. A filter-trust-region method for unconstrained optimization. SIAM J Optim, 16: 341-357 (2005).
    • (2005) SIAM J Optim , vol.16 , pp. 341-357
    • Gould, N.I.M.1    Sainvitu, C.2    Toint, P.L.3
  • 26
    • 71249107743 scopus 로고    scopus 로고
    • A dwindling filter line-search method for unconstrained optimization
    • Nanjing Normal University, School of Mathematics and Computer Science
    • Chen Y N, Sun W. A dwindling filter line-search method for unconstrained optimization. Technical Report Opt-06-11, School of Mathematics and Computer Science, Nanjing Normal University, 2006.
    • (2006) Technical Report Opt-06-11
    • Chen, Y.N.1    Sun, W.2
  • 28
    • 48249101108 scopus 로고    scopus 로고
    • A filter-trust-region method for unconstrained optimization
    • Miao W, Sun W. A filter-trust-region method for unconstrained optimization. Numer Math J Chinese Univ, 29: 88-96 (2007).
    • (2007) Numer Math J Chinese Univ , vol.29 , pp. 88-96
    • Miao, W.1    Sun, W.2
  • 29
    • 71249150942 scopus 로고    scopus 로고
    • On filter-type methods for optimization: Motivation and development
    • Taiwan: Cheng Kung University
    • Sun W. On filter-type methods for optimization: motivation and development. An invited talk, 4th Sino-Japanese Optimization Meeting (SJOM2008), August 26-31, 2008. Cheng Kung University, Taiwan.
    • (2008) An Invited Talk, 4th Sino-Japanese Optimization Meeting (SJOM2008)
    • Sun, W.1
  • 32
    • 3142743708 scopus 로고    scopus 로고
    • Solving semidefinite quadratic-linear programs using SDPT3
    • Tutuncu R H, Toh K C, Todd M J. Solving semidefinite quadratic-linear programs using SDPT3. Math Program, 95: 189-217 (2003).
    • (2003) Math Program , vol.95 , pp. 189-217
    • Tutuncu, R.H.1    Toh, K.C.2    Todd, M.J.3
  • 34
    • 34548542111 scopus 로고    scopus 로고
    • An unconstrained optimization method using nonmonotone second order Goldstein's line search
    • Sun W, Zhou Q Y. An unconstrained optimization method using nonmonotone second order Goldstein's line search. Sci China Ser A, 50: 1389-1400 (2007).
    • (2007) Sci China Ser A , vol.50 , pp. 1389-1400
    • Sun, W.1    Zhou, Q.Y.2
  • 35
    • 0012036339 scopus 로고
    • A nonmonotone trust region algorithm for equality constrained optimization
    • Ke X W, Han J Y. A nonmonotone trust region algorithm for equality constrained optimization. Sci China Ser A, 38: 683-695 (1995).
    • (1995) Sci China Ser A , vol.38 , pp. 683-695
    • Ke, X.W.1    Han, J.Y.2
  • 38
    • 0033296702 scopus 로고    scopus 로고
    • SDPLIB 1.2, a library of semidefinite programming test problems
    • Borchers B. SDPLIB 1. 2, a library of semidefinite programming test problems. Optim Methods Softw, 11: 597-611 (1999).
    • (1999) Optim Methods Softw , vol.11 , pp. 597-611
    • Borchers, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.