Global Convergence of a Trust Region Algorithm for Nonlinear Inequality Constrained Optimization Problems

References

• An , L. T. H. and Tao , P. D. 1998a . A d. c. optimization algorithm for solving the trust region subproblem . SIAM J. Optim. , 8 : 476 – 505 .
   Web of Science ®Google Scholar
• An , L. T. H. and Tao , P. D. 1998b . A branch-and-bound method via d.c. optimization algorithm and ellipsoidal technique for box constrained nonconvex quadratic programming problems . J. Global Optim. , 13 : 171 – 206 .
   Web of Science ®Google Scholar
• Boggs , P. T. , Kearsley , A. J. and Tolle , J. M. 1999a . A global convergence analysis of an algorithm for large scale nonlinear optimization problem . SIAM J. Optim. , 9 : 833 – 862 .
   Web of Science ®Google Scholar
• Boggs , P. T. , Kearsley , A. J. and Tolle , J. M. 1999b . A practical algorithm for general large scale nonlinear optimization problem . SIAM J. Optim. , 9 : 755 – 778 .
   Web of Science ®Google Scholar
• Burke , J. V. , More , J. J. and Toraldo , G. 1990 . Convergence properties of trust region method for linear and convex constraints . Math. Programming , 47 : 305 – 336 .
   Web of Science ®Google Scholar
• Byrd , R. H. , Schnabel , R. B. and Shultz , G. A. 1987 . A trust region algorithm for nonlinearly constrained optimization . SIAM J. Numer. Anal. , 24 : 1152 – 1170 .
   Web of Science ®Google Scholar
• Byrd , R. H. , Gilbert , J. C. and Nocedal , J. 2000 . A trust region method based on interior point techniques for nonlinear programming . Math. Programming , 89 : 149 – 185 .
   Web of Science ®Google Scholar
• Conn , A. R. , Gould , N. I. M. and Toint , Ph. L. 1988 . Global convergence of a class of trust region algorithms for optimization with simple bounds . SIAM J. Numer. Anal. , 25 : 433 – 460 .
   Web of Science ®Google Scholar
• Conn , A. R. , Gould , N. I. M. , Sartenaer , A. and Toint , Ph. L. 1993 . Global convergence of a class of trust region algorithms for optimization using inexact projections on convex constraints . SIAM J. Optim. , 3 : 164 – 221 .
   Web of Science ®Google Scholar
• Conn , A. R. , Gould , N. , Orban , D. and Toint , Ph. L. 2000a . A primal-dual trust-region algorithm for non-convex nonlinear programming . Math. Programming , 87 : 215 – 249 .
   Web of Science ®Google Scholar
• Conn , A. R. , Gould , N. I. M. and Toint , Ph. L. 2000b . “ Trust region methods ” . In MPS-SIAM Series on Optimization Philadelphia, PA
   Google Scholar
• Dennis , J. E. and Vicente , L. N. 1997 . On the convergence theory of trust-region based algorithms for equality-constrained optimization . SIAM J. Optim. , 7 : 927 – 950 .
   Web of Science ®Google Scholar
• Dennis , J. M. Jr. , El-Alem , M. and Maciel , M. C. 1997 . A global convergence theory for general trust-region-based algorithm for equality constrained optimization . SIAM J. Optim. , 7 : 177 – 207 .
   Web of Science ®Google Scholar
• Dennis , J. M. Jr. , El-Alem , M. and Williamson , K. 1999 . A trust region approach to non-linear system of equalities and inequalities . SIAM J. Optim. , 9 : 291 – 315 .
   Web of Science ®Google Scholar
• El-Alem , M. M. 1991 . A global convergence theory for the Celis-Dennis-Tapia trust-region algorithm for constrained optimization . SIAM J. Numer. Anal. , 28 : 266 – 290 .
   Web of Science ®Google Scholar
• El-Alem , M. M. 1995 . A robust trust-region algorithm with a nonmonotonic penalty parameter scheme for constrained optimization . SIAM J. Optim. , 5 : 348 – 378 .
   Web of Science ®Google Scholar
• Friedlander , A. , Martinez , J. M. and Santos , S. A. 1994 . A new trust region algorithm for bound constrained minimization . Appl. Math. Optim. , 30 : 235 – 266 .
   Web of Science ®Google Scholar
• Gauvin , J. 1977 . A necessary and sufficient regularity condition to have bounded multipliers in nonconvex programming . Math. Programming , 12 : 136 – 138 .
   Web of Science ®Google Scholar
• Gay , D. M. 1984 . “ A trust region approach to linearly constrained optimization ” . In Numerical Analysis Proceeding Dundee 1983 , Lecture Notes in Mathematics 1066 Edited by: Griffiths , D. F. 72 – 105 . Berlin : Spring-Verlag .
   Google Scholar
• Gomes , F. M. , Maciel , M. C. and Martinez , J. M. 1999 . Nonlinear programming algorithms using trust regions and augmented lagrangians with nonmonotone penalty parameters . Math. Programming , 84 : 161 – 200 .
   Web of Science ®Google Scholar
• Han , S. P. and Mangasarian , O. L. 1983 . A dual differentiable exact penalty function . Math. Programming , 25 : 293 – 306 .
   Web of Science ®Google Scholar
• Kelley , C. T. 1999 . Iteration Methods for Optimization, Frontiers in Applied Mathematics Philadelphia, PA : SIAM .
   Google Scholar
• Lalee , M. , Nocedal , J. and Plantenga , T. 1998 . On the implamentation of an algorithm for large scale equality constrained optimization . SIAM J. Optim. , 8 : 682 – 706 .
   Web of Science ®Google Scholar
• Martinez , J. M. 1998 . A two-phase trust region model algorithm with global convergence for nonlinear programming . J. Optim. Theory Appl. , 96 : 397 – 436 .
   Web of Science ®Google Scholar
• Martinez , J. M. and Santos , S. A. 1995 . A trust-region strategy for minimization on arbitrary domains . Math. Programming , 68 : 267 – 301 .
   Web of Science ®Google Scholar
• Martinez , J. M. and Pilotta , E. A. 2000 . Inexact-restoration algorithm for constrained optimization . J. Optim. Theory Appl. , 104 : 135 – 163 .
   Web of Science ®Google Scholar
• Moré , J. J. 1983 . “ Recent developments in algorithms and software for trust region methods ” . In Mathematical Programming, the State of the Art 258 – 287 . Berlin : Springer-Verlag .
   Google Scholar
• Moré , J. J. and Sorensen , D. C. 1983 . Computing a trust region step . SIAM J. Sci. Stast. Comput. , 4 : 553 – 572 .
   Web of Science ®Google Scholar
• Omojokun , E. O. 1989 . “ Trust Region Algorithms for Optimization with Nonlinear Equality and Inequality Constraints ” . Ph.D thesis, University of Colorado at Boulder USA
   Google Scholar
• Powell , M. J. D. 1970 . “ A new algorithm for unconstrained optimization ” . In Nonlinear Programming Edited by: Rosen , J. B. , Mangasarian , O. L. and Ritter , K. 31 – 66 . New York : Academic Press .
   Google Scholar
• Powell , M. J. D. 1975 . “ Convergence properties of a class of minimization algorithms ” . In Nonlinear Programming 2 Edited by: Mangasarian , O. L. , Meyer , R. and Robinson , S. 1 – 27 . New York : Academic Press .
   Google Scholar
• Powell , M. J. D. and Yuan , Y. 1991 . A trust region algorithm for equality constrained optimization . Math. Programming , 49 : 189 – 211 .
   Web of Science ®Google Scholar
• Sartenaer , A. 1995 . A class of trust region methods for nonlinear network optimization problems . SIAM J. Optim. , 5 : 379 – 407 .
   Web of Science ®Google Scholar
• Sorensen , D. C. 1982 . “ Trust region methods for unconstrained optimization ” . In Nonlinear Optimization 1981 Edited by: Powell , M. J. D. 29 – 38 . London : Academic Press .
   Google Scholar
• Sorensen , D. C. 1997 . Minimization of a large scale quadratic function subject to a spherical constraint . SIAM J. Optim. , 7 : 141 – 161 .
   Web of Science ®Google Scholar
• Toint , P. 1988 . Global convergence of a class of trust region methods for non-convex minimization in Hilbert spaces . IMA J. Numer. Anal. , 8 : 231 – 252 .
   Web of Science ®Google Scholar
• Vardi , A. 1985 . A trust region algorithm for equality constrained minimization: Convergence properties and implementation . SIAM J. Numer. Anal. , 22 : 575 – 591 .
   Web of Science ®Google Scholar
• Wolfe , P. 1961 . A duality theorem for nonlinear programming . Q. Appl. Math. , 19 : 239 – 244 .
   Google Scholar
• Yin , H. and Han , J. 2003 . An interior-point trust-region algorithm for bound constrained minimization problems . J. Syst. Sci. Inf. , 1 : 431 – 445 .
   Google Scholar
• Yuan , Y. 1993 . “ A trust region algorithm for nonlinear optimization ” . In Proceedings of the First International Colloquium on Numerical Analysis Edited by: Bainov , D. and Covachev , V. 141 – 152 . VSP : Zeist .
   Google Scholar