메뉴 건너뛰기




Volumn 13, Issue 2, 2003, Pages 432-469

Convergent infeasible interior-point trust-region methods for constrained minimization

Author keywords

First and second order stationary points; Interior point method; Log barrier function; Nonlinear program; Semidefinite programming; Trust region strategy

Indexed keywords


EID: 0038811730     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623499357945     Document Type: Review
Times cited : (20)

References (45)
  • 2
    • 0003169116 scopus 로고
    • Interior point methods in semidefinite programming with applications to combinatorial optimization
    • F. ALIZADEH, Interior point methods in semidefinite programming with applications to combinatorial optimization, SIAM J. Optim., 5 (1995), pp. 13-51.
    • (1995) SIAM J. Optim. , vol.5 , pp. 13-51
    • Alizadeh, F.1
  • 3
    • 0018523346 scopus 로고
    • Penalty methods for computing points that satisfy second order necessary points
    • A. AUSLENDER, Penalty methods for computing points that satisfy second order necessary points, Math. Programming, 17 (1979), pp. 229-238.
    • (1979) Math. Programming , vol.17 , pp. 229-238
    • Auslender, A.1
  • 4
    • 0039772219 scopus 로고    scopus 로고
    • Solving large-scale sparse semidefinite programs for combinatorial optimization
    • S. J. BENSON, Y. YE, AND X. ZHANG, Solving large-scale sparse semidefinite programs for combinatorial optimization, SIAM J. Optim., 10 (2000), pp. 443-461.
    • (2000) SIAM J. Optim. , vol.10 , pp. 443-461
    • Benson, S.J.1    Ye, Y.2    Zhang, X.3
  • 6
    • 0001130234 scopus 로고    scopus 로고
    • A trust region method based on interior point techniques for nonlinear programming
    • R. H. BYRD, J. C. GILBERT, AND J. NOCEDAL, A trust region method based on interior point techniques for nonlinear programming, Math. Program., 89 (2000), pp. 149-185.
    • (2000) Math. Program. , vol.89 , pp. 149-185
    • Byrd, R.H.1    Gilbert, J.C.2    Nocedal, J.3
  • 7
    • 0033471382 scopus 로고    scopus 로고
    • An interior point algorithm for large-scale nonlinear programming
    • R. H. BYRD, M. E. HRIBAR, AND J. NOCEDAL, An interior point algorithm for large-scale nonlinear programming, SIAM J. Optim., 9 (1999), pp. 877-900.
    • (1999) SIAM J. Optim. , vol.9 , pp. 877-900
    • Byrd, R.H.1    Hribar, M.E.2    Nocedal, J.3
  • 8
    • 0012691880 scopus 로고    scopus 로고
    • On the local behavior of an interior point method for nonlinear programming
    • D. P. Griffiths and D. J. Higham, eds., Addison Wesley Longman, Reading, MA
    • R. H. BYRD, G. LIU, AND J. NOCEDAL, On the local behavior of an interior point method for nonlinear programming, in Numerical Analysis 1997, D. P. Griffiths and D. J. Higham, eds., Addison Wesley Longman, Reading, MA, 1998, pp. 37-56.
    • (1998) Numerical Analysis 1997 , pp. 37-56
    • Byrd, R.H.1    Liu, G.2    Nocedal, J.3
  • 10
    • 0034599835 scopus 로고    scopus 로고
    • A reduced space interior point strategy for optimization of differential algebraic systems
    • A. M. CERVANTES, A. WÄCHTER, R. TÜTÜNCÜ, AND L. T. BIEGLER, A reduced space interior point strategy for optimization of differential algebraic systems, Comput. Chem. Eng., 24 (2000), pp. 39-51.
    • (2000) Comput. Chem. Eng. , vol.24 , pp. 39-51
    • Cervantes, A.M.1    Wächter, A.2    Tütüncü, R.3    Biegler, L.T.4
  • 11
    • 0030303844 scopus 로고    scopus 로고
    • An interior trust region approach for nonlinear minimization subject to bounds
    • T. F. COLEMAN AND Y. Li, An interior trust region approach for nonlinear minimization subject to bounds, SIAM J. Optim., 6 (1996), pp. 418-445.
    • (1996) SIAM J. Optim. , vol.6 , pp. 418-445
    • Coleman, T.F.1    Li, Y.2
  • 12
    • 0000317378 scopus 로고    scopus 로고
    • A primal-dual trust-region algorithm for non-convex nonlinear programming
    • A. R. CONN, N. I. M. GOULD, D. ORBAN, AND P. L. TOINT, A primal-dual trust-region algorithm for non-convex nonlinear programming, Math. Program., 87 (2000), pp. 215-249.
    • (2000) Math. Program. , vol.87 , pp. 215-249
    • Conn, A.R.1    Gould, N.I.M.2    Orban, D.3    Toint, P.L.4
  • 13
    • 0002443848 scopus 로고    scopus 로고
    • A primal-dual algorithm for minimizing a non-convex function subject to bound and linear equality constraints
    • G. Di Pillo and F. Giannessi, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands
    • A. R. CONN, N. I. M. GOULD, AND P. L. TOINT, A primal-dual algorithm for minimizing a non-convex function subject to bound and linear equality constraints, in Nonlinear Optimization and Related Topics, G. Di Pillo and F. Giannessi, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000, pp. 15-49.
    • (2000) Nonlinear Optimization and Related Topics , pp. 15-49
    • Conn, A.R.1    Gould, N.I.M.2    Toint, P.L.3
  • 15
    • 0032165036 scopus 로고    scopus 로고
    • Trust-region interior-point SQP algorithms for a class of nonlinear programming problems
    • J. E. DENNIS, M. HEINKENSCHLOSS, AND L. N. VICENTE, Trust-region interior-point SQP algorithms for a class of nonlinear programming problems, SIAM J. Control Optim., 36 (1998), pp. 1750-1794.
    • (1998) SIAM J. Control Optim. , vol.36 , pp. 1750-1794
    • Dennis, J.E.1    Heinkenschloss, M.2    Vicente, L.N.3
  • 16
    • 0021794572 scopus 로고
    • A continuously differentiable exact penalty function for nonlinear programming problems with inequality constraints
    • G. Di PILLO AND L. GRIPPO, A continuously differentiable exact penalty function for nonlinear programming problems with inequality constraints, SIAM J. Control Optim., 23 (1985), pp. 72-84.
    • (1985) SIAM J. Control Optim. , vol.23 , pp. 72-84
    • Di Pillo, G.1    Grippo, L.2
  • 17
    • 0030541525 scopus 로고    scopus 로고
    • On the formulation and theory of the Newton interior-point method for nonlinear programming
    • A. S. EL-BAKRY, R. A. TAPIA, T. TSUCHIYA, AND Y. ZHANG, On the formulation and theory of the Newton interior-point method for nonlinear programming, J. Optim. Theory Appl., 89 (1996), pp. 507-541.
    • (1996) J. Optim. Theory Appl. , vol.89 , pp. 507-541
    • El-Bakry, A.S.1    Tapia, R.A.2    Tsuchiya, T.3    Zhang, Y.4
  • 18
    • 0032131216 scopus 로고    scopus 로고
    • Convergence to second order stationary points in inequality constrained optimization
    • F. FACCHINEI AND S. LUCIDI, Convergence to second order stationary points in inequality constrained optimization, Math. Oper. Res., 23 (1998), pp. 746-766.
    • (1998) Math. Oper. Res. , vol.23 , pp. 746-766
    • Facchinei, F.1    Lucidi, S.2
  • 20
    • 0021459322 scopus 로고
    • Semi-definite matrix constraints in optimization
    • R. FLETCHER, Semi-definite matrix constraints in optimization, SIAM J. Control Optim., 23 (1985), pp. 493-513.
    • (1985) SIAM J. Control Optim. , vol.23 , pp. 493-513
    • Fletcher, R.1
  • 21
    • 0031542934 scopus 로고    scopus 로고
    • Newton methods for large-scale linear inequality-constrained minimization
    • A. FORSGREN AND W. MURRAY, Newton methods for large-scale linear inequality-constrained minimization, SIAM J. Optim., 7 (1997). pp. 162-176.
    • (1997) SIAM J. Optim. , vol.7 , pp. 162-176
    • Forsgren, A.1    Murray, W.2
  • 22
    • 0032358968 scopus 로고    scopus 로고
    • Primal-dual interior methods for nonconvex nonlinear programming
    • A. FORSGREN AND P. E. GILL, Primal-dual interior methods for nonconvex nonlinear programming, SIAM J. Optim., 8 (1998), pp. 1132-1152.
    • (1998) SIAM J. Optim. , vol.8 , pp. 1132-1152
    • Forsgren, A.1    Gill, P.E.2
  • 23
    • 0002688960 scopus 로고    scopus 로고
    • A primal-dual interior method for nonconvex nonlinear programming
    • Kluwer Academic Publishers, Dordrecht, The Netherlands
    • D. M. GAY, M. L. OVERTON, AND M. H. WRIGHT, A primal-dual interior method for nonconvex nonlinear programming, in Advances in Nonlinear Programming, Appl. Optim. 14, Kluwer Academic Publishers, Dordrecht, The Netherlands. 1998, pp. 31-56.
    • (1998) Advances in Nonlinear Programming, Appl. Optim. , vol.14 , pp. 31-56
    • Gay, D.M.1    Overton, M.L.2    Wright, M.H.3
  • 24
    • 0018522912 scopus 로고
    • A multiplier method with automatic limitation of penalty growth
    • T. GLAD AND E. POLAK, A multiplier method with automatic limitation of penalty growth, Math Programming, 17 (1979), pp. 140-155.
    • (1979) Math Programming , vol.17 , pp. 140-155
    • Glad, T.1    Polak, E.2
  • 25
    • 0035603909 scopus 로고    scopus 로고
    • Superlinear convergence of primal-dual interior point algorithms for nonlinear programming
    • N. I. M. GOULD, D. ORBAN, A. SARTENAER, AND PH. L. TOINT, Superlinear convergence of primal-dual interior point algorithms for nonlinear programming, SIAM J. Optim., 11 (2001), pp. 974-1002.
    • (2001) SIAM J. Optim. , vol.11 , pp. 974-1002
    • Gould, N.I.M.1    Orban, D.2    Sartenaer, A.3    Toint, Ph.L.4
  • 26
    • 0037572858 scopus 로고    scopus 로고
    • A note on the second-order convergence of optimization algorithms using barrier functions
    • N. I. M. GOULD AND PH. L. TOINT, A note on the second-order convergence of optimization algorithms using barrier functions, Math. Program., 85 (1999), pp. 433-438.
    • (1999) Math. Program. , vol.85 , pp. 433-438
    • Gould, N.I.M.1    Toint, Ph.L.2
  • 28
    • 0008996079 scopus 로고    scopus 로고
    • Technical report, Institut für Angewandte Mathematik und Statistik, Universität Würzburg, Würzburg, Germany
    • F. JARRE, A QQP-minimization method for semidefinite and smooth nonconvex programs, Technical report, Institut für Angewandte Mathematik und Statistik, Universität Würzburg, Würzburg, Germany, 1998.
    • (1998) A QQP-Minimization Method for Semidefinite and Smooth Nonconvex Programs
    • Jarre, F.1
  • 29
    • 0000547919 scopus 로고
    • Primal-dual and primal interior point, algorithms for general nonlinear programs
    • L. S. LASDON. J. PLUMMER, AND G. YU, Primal-dual and primal interior point, algorithms for general nonlinear programs, ORSA J. Comput., 7 (1995), pp. 321-332.
    • (1995) ORSA J. Comput. , vol.7 , pp. 321-332
    • Lasdon, L.S.1    Plummer, J.2    Yu, G.3
  • 30
    • 0012035936 scopus 로고    scopus 로고
    • Trust region affine scaling algorithms for linearly constrained convex and concave programs
    • R. D. C. MONTEIRO AND Y. WANG, Trust region affine scaling algorithms for linearly constrained convex and concave programs, Math. Programming, 80 (1998), pp. 283-313.
    • (1998) Math. Programming , vol.80 , pp. 283-313
    • Monteiro, R.D.C.1    Wang, Y.2
  • 32
    • 0018106354 scopus 로고
    • A second-order method for the general nonlinear programming problem
    • H. MUKAI AND E. POLAK, A second-order method for the general nonlinear programming problem, J. Optim. Theory Appl., 26 (1978), pp. 515-532.
    • (1978) J. Optim. Theory Appl. , vol.26 , pp. 515-532
    • Mukai, H.1    Polak, E.2
  • 33
    • 0023452095 scopus 로고
    • Some NP-complete problems in quadratic and nonlinear programming
    • K. G. MURTY AND S. N. KABADI, Some NP-complete problems in quadratic and nonlinear programming, Math. Programming. 39 (1987), pp. 117-129.
    • (1987) Math. Programming , vol.39 , pp. 117-129
    • Murty, K.G.1    Kabadi, S.N.2
  • 34
    • 0003254248 scopus 로고
    • Interior-point polynomial algorithms in convex programming
    • Siam, Philadelphia
    • Y. NESTEROV AND A. NEMIROVSKII, Interior-Point Polynomial Algorithms in Convex Programming, SIAM Stud. Appl. Math. 13, SIAM, Philadelphia, 1994.
    • (1994) Siam Stud. Appl. Math. , vol.13
    • Nesterov, Y.1    Nemirovskii, A.2
  • 35
    • 0038248478 scopus 로고    scopus 로고
    • private communication, CERFACS, Toulouse, France
    • D. ORBAN, private communication, CERFACS, Toulouse, France, 2000.
    • (2000)
    • Orban, D.1
  • 36
    • 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
  • 38
    • 0030106462 scopus 로고    scopus 로고
    • Semidefinite programming
    • L. VANDENBERGHE AND S. BOYD, Semidefinite programming, SIAM Rev., 38 (1996), pp. 49-95.
    • (1996) SIAM Rev. , vol.38 , pp. 49-95
    • Vandenberghe, L.1    Boyd, S.2
  • 39
    • 0000287204 scopus 로고    scopus 로고
    • An interior-point algorithm for nonconvex nonlinear programming
    • R. V. VANDERBEI AND D. F. SHANNO, An interior-point algorithm for nonconvex nonlinear programming, Comput. Optim. Appl., 13 (1999), pp. 231-252.
    • (1999) Comput. Optim. Appl. , vol.13 , pp. 231-252
    • Vanderbei, R.V.1    Shanno, D.F.2
  • 40
    • 0000892372 scopus 로고    scopus 로고
    • Failure of global convergence for a class of interior point methods for nonlinear programming
    • A. WÄCHTER AND L. T. BIEGLER, Failure of global convergence for a class of interior point methods for nonlinear programming, Math. Programming, 88 (2000), pp. 565-574.
    • (2000) Math. Programming , vol.88 , pp. 565-574
    • Wächter, A.1    Biegler, L.T.2
  • 43
    • 0000273506 scopus 로고    scopus 로고
    • Superlinear and quadratic convergence of some primal-dual interior point methods for constrained optimization
    • H. YAMASHITA AND H. YABE, Superlinear and quadratic convergence of some primal-dual interior point methods for constrained optimization, Math. Programming, 75 (1996), pp. 377-397.
    • (1996) Math. Programming , vol.75 , pp. 377-397
    • Yamashita, H.1    Yabe, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.