메뉴 건너뛰기




Volumn 156, Issue 1, 2004, Pages 159-174

Nonmonotone trust region method for solving optimization problems

Author keywords

Nonlinear programming; Nonmonotone optimization method; Quasi Newton method; Trust region method

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; MATHEMATICAL MODELS; NONLINEAR PROGRAMMING; OPTIMIZATION; ROBUSTNESS (CONTROL SYSTEMS); SET THEORY;

EID: 3843055668     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2003.07.008     Document Type: Article
Times cited : (76)

References (35)
  • 1
    • 0023430609 scopus 로고
    • A trust region algorithm for nonlinearly constrained optimization
    • Byrd R.H., Schnabel R.B., Shultz G.A. A trust region algorithm for nonlinearly constrained optimization. SIAM J. Numer. Anal. 24:1987;1152-1170.
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 1152-1170
    • Byrd, R.H.1    Schnabel, R.B.2    Shultz, G.A.3
  • 2
    • 0002674910 scopus 로고
    • The watchdog technique for forcing convergence in algorithms for constrained optimization
    • Chamberlain R.M., Powell M.J.D., Lemarechal C., Pedersen H.C. The watchdog technique for forcing convergence in algorithms for constrained optimization. Math. Program. Study. 16:1982;1-17.
    • (1982) Math. Program. Study , vol.16 , pp. 1-17
    • Chamberlain, R.M.1    Powell, M.J.D.2    Lemarechal, C.3    Pedersen, H.C.4
  • 3
    • 33645392399 scopus 로고
    • A unified approach to global convergence of trust region methods for nonsmooth optimization
    • Dennis J.E., Li S.B., Tapia R.A. A unified approach to global convergence of trust region methods for nonsmooth optimization. Math. Program. 68:1995;319-346.
    • (1995) Math. Program. , vol.68 , pp. 319-346
    • Dennis, J.E.1    Li, S.B.2    Tapia, R.A.3
  • 5
    • 0030418954 scopus 로고    scopus 로고
    • Trust region method for conic model to solve unconstrained optimization
    • Di S., Sun W. Trust region method for conic model to solve unconstrained optimization. Optim. Meth. Software. 6:1996;237-263.
    • (1996) Optim. Meth. Software , vol.6 , pp. 237-263
    • Di, S.1    Sun, W.2
  • 6
    • 0000017341 scopus 로고
    • An algorithm for solving linearly constrained optimization problems
    • Fletcher R. An algorithm for solving linearly constrained optimization problems. Math. Program. 2:1972;133-165.
    • (1972) Math. Program. , vol.2 , pp. 133-165
    • Fletcher, R.1
  • 8
    • 0001963239 scopus 로고
    • A model algorithm for composite nondifferentiable optimization problems
    • A model algorithm for composite nondifferentiable optimization problems, Mathematical Programming Study 17 (1982) 67-76.
    • (1982) Mathematical Programming Study , vol.17 , pp. 67-76
  • 9
    • 0013111241 scopus 로고
    • A trust region method for constrained nonsmooth equations
    • W.W. et al. Hager. Kluwer Academic Publisher
    • Gabrial S.A., Pang J.S. A trust region method for constrained nonsmooth equations. Hager W.W., et al. Large Scale Optimization: State of the Art. 1994;155-181 Kluwer Academic Publisher.
    • (1994) Large Scale Optimization: State of the Art , pp. 155-181
    • Gabrial, S.A.1    Pang, J.S.2
  • 10
    • 0000955796 scopus 로고
    • Computing optimal locally constrained step
    • Gay D.M. Computing optimal locally constrained step. SIAM J. Sci. Stat. Comput. 2:1981;186-197.
    • (1981) SIAM J. Sci. Stat. Comput. , vol.2 , pp. 186-197
    • Gay, D.M.1
  • 11
    • 0001237594 scopus 로고
    • Maximization by quadratic hill climbing
    • Goldfeld S., Quandt R., Trotter H. Maximization by quadratic hill climbing. Econometrica. 34:1966;541-551.
    • (1966) Econometrica , vol.34 , pp. 541-551
    • Goldfeld, S.1    Quandt, R.2    Trotter, H.3
  • 12
    • 0022766519 scopus 로고
    • A nonmonotone line search technique for Newton's method
    • Grippo L., Lampariello F., Lucidi S. A nonmonotone line search 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
  • 13
    • 0000843862 scopus 로고
    • A truncated Newton method with nonmonotone line search for unconstrained optimization
    • Grippo L., Lampariello F., Lucidi S. A truncated Newton method with nonmonotone line search for unconstrained optimization. J. Optim. Theory Appl. 60:1989;401-419.
    • (1989) J. Optim. Theory Appl. , vol.60 , pp. 401-419
    • Grippo, L.1    Lampariello, F.2    Lucidi, S.3
  • 14
    • 0000873069 scopus 로고
    • A method for the solution of certain nonlinear problems in least squares
    • Levenberg K. A method for the solution of certain nonlinear problems in least squares. Quart. Appl. Math. 2:1944;164-168.
    • (1944) Quart. Appl. Math. , vol.2 , pp. 164-168
    • Levenberg, K.1
  • 15
    • 84948267485 scopus 로고
    • Global convergence of BFGS algorithm with nonmonotone linesearch
    • Liu G., Han J., Sun D. Global convergence of BFGS algorithm with nonmonotone linesearch. Optimization. 34:1995;147-159.
    • (1995) Optimization , vol.34 , pp. 147-159
    • Liu, G.1    Han, J.2    Sun, D.3
  • 16
    • 0000169232 scopus 로고
    • An algorithm for least squares estimation of nonlinear parameters
    • Marquardt D.W. An algorithm for least squares estimation of nonlinear parameters. SIAM J. Appl. Math. 11:1963;431-441.
    • (1963) SIAM J. Appl. Math. , vol.11 , pp. 431-441
    • Marquardt, D.W.1
  • 17
    • 0003162836 scopus 로고
    • Recent development in algorithm and software for trust region methods
    • A. Bachem, M. Grotschel, & B. Kortz. Berlin: Springer-Verlag
    • Moré J.J. Recent development in algorithm and software for trust region methods. Bachem A., Grotschel M., Kortz B. Mathematical Programming: The State of the Art. 1983;258-285 Springer-Verlag, Berlin.
    • (1983) Mathematical Programming: The State of the Art , pp. 258-285
    • Moré, J.J.1
  • 20
    • 0003098115 scopus 로고
    • Minimization of locally Lipschitzian functions
    • Pang J.S., Han S.P., Rangaraj N. Minimization of locally Lipschitzian functions. SIAM J. Optim. 1:1991;57-82.
    • (1991) SIAM J. Optim. , vol.1 , pp. 57-82
    • Pang, J.S.1    Han, S.P.2    Rangaraj, N.3
  • 21
    • 0002302301 scopus 로고
    • Convergence properties of a class of minimization algorithms
    • O.L. Mangasarian, R.R. Meyer, RobinsonS.M. New York: Academic Press
    • Powell M.J.D. Convergence properties of a class of minimization algorithms. Mangasarian O.L., Meyer R.R., Robinson S.M. Nonlinear Programming 2. 1975;Academic Press, New York.
    • (1975) Nonlinear Programming , vol.2
    • Powell, M.J.D.1
  • 22
    • 0021482384 scopus 로고
    • On the global convergence of trust region algorithms for unconstrained optimization
    • Powell M.J.D. On the global convergence of trust region algorithms for unconstrained optimization. Math. Program. 29:1984;297-303.
    • (1984) Math. Program. , vol.29 , pp. 297-303
    • Powell, M.J.D.1
  • 23
    • 0025540157 scopus 로고
    • A trust region algorithm for equality constrained optimization
    • Powell M.J.D., Yuan Y. A trust region algorithm for equality constrained optimization. Math. Prog. 49:1990;189-213.
    • (1990) Math. Prog. , vol.49 , pp. 189-213
    • Powell, M.J.D.1    Yuan, Y.2
  • 24
    • 0028480086 scopus 로고
    • A trust region algorithm for minimization of locally Lipschitzian function
    • Qi L., Sun J. A trust region algorithm for minimization of locally Lipschitzian function. Math. Prog. 66:1994;25-43.
    • (1994) Math. Prog. , vol.66 , pp. 25-43
    • Qi, L.1    Sun, J.2
  • 25
    • 0010200325 scopus 로고    scopus 로고
    • On the trust region algorithm for nonsmooth optimization
    • Sampaio R.J.B., Sun W., Yuan J. On the trust region algorithm for nonsmooth optimization. Appl. Math. Comput. 85:1997;109-116.
    • (1997) Appl. Math. Comput. , vol.85 , pp. 109-116
    • Sampaio, R.J.B.1    Sun, W.2    Yuan, J.3
  • 26
    • 0042112291 scopus 로고    scopus 로고
    • On non-quadratic model methods for optimization
    • Sun W. On non-quadratic model methods for optimization. Asia Pacific J. Oper. Res. 13:1996;43-63.
    • (1996) Asia Pacific J. Oper. Res. , vol.13 , pp. 43-63
    • Sun, W.1
  • 27
    • 3843076622 scopus 로고    scopus 로고
    • Trust region methods with quasi-Newton update for non-smooth least-squares problems
    • Sun W., Sampaio R.J.B., Yuan J. Trust region methods with quasi-Newton update for non-smooth least-squares problems. Appl. Math. Comput. 105:1999;772-775.
    • (1999) Appl. Math. Comput. , vol.105 , pp. 772-775
    • Sun, W.1    Sampaio, R.J.B.2    Yuan, J.3
  • 28
    • 0036723742 scopus 로고    scopus 로고
    • On global convergence of nonmonotone descent methods
    • Sun W., Han J., Sun J. On global convergence of nonmonotone descent methods. J. Comput. Appl. Math. 146:2002;89-98.
    • (2002) J. Comput. Appl. Math. , vol.146 , pp. 89-98
    • Sun, W.1    Han, J.2    Sun, J.3
  • 29
    • 0001019976 scopus 로고    scopus 로고
    • An assessment of non-monotone linesearch techniques for unconstrained optimization
    • Toint Ph.L. An assessment of non-monotone linesearch techniques for unconstrained optimization. SIAM J. Sci. Stat. Comput. 17:1996;725-739.
    • (1996) SIAM J. Sci. Stat. Comput. , vol.17 , pp. 725-739
    • Toint, Ph.L.1
  • 30
    • 0022076594 scopus 로고
    • A trust region algorithm for equality constrained minimization: Convergence properties and implementation
    • Vardi A. A trust region algorithm for equality constrained minimization: convergence properties and implementation. SIAM Numer. Anal. 22:1985;575-591.
    • (1985) SIAM Numer. Anal. , vol.22 , pp. 575-591
    • Vardi, A.1
  • 31
    • 0022010767 scopus 로고
    • Conditions for convergence of trust region algorithms for nonsmooth optimization
    • Yuan Y. Conditions for convergence of trust region algorithms for nonsmooth optimization. Math. Program. 31:1985;220-228.
    • (1985) Math. Program. , vol.31 , pp. 220-228
    • Yuan, Y.1
  • 32
    • 0002765829 scopus 로고
    • On a subproblem of trust region algorithms for constrained optimization
    • Yuan Y. On a subproblem of trust region algorithms for constrained optimization. Math. Program. 47:1990;53-63.
    • (1990) Math. Program. , vol.47 , pp. 53-63
    • Yuan, Y.1
  • 34
    • 0033436975 scopus 로고    scopus 로고
    • Trust region dogleg path algorithm for unconstrained minimization
    • Zhang J., Xu C. Trust region dogleg path algorithm for unconstrained minimization. Ann. Oper. Res. 87:1999;407-418.
    • (1999) Ann. Oper. Res. , vol.87 , pp. 407-418
    • Zhang, J.1    Xu, C.2
  • 35
    • 0025517082 scopus 로고
    • Projected quasi-Newton algorithm with trust-region for constrained optimization
    • Zhang J., Zhu D. Projected quasi-Newton algorithm with trust-region for constrained optimization. J. Optim. Theory Appl. 67:1990;369-393.
    • (1990) J. Optim. Theory Appl. , vol.67 , pp. 369-393
    • Zhang, J.1    Zhu, D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.