An active-set trust-region method for derivative-free nonlinear bound-constrained optimization

References

• Burdakov , O. 1995 . “ An MST-type algorithm for the optimal basis problem ” . In Technical Report TR/PA/95/22, CERFACS, 42, av. G. Coriolis, 31057 Toulouse France
   Google Scholar
• Burdakov , O. 1997 . A greedy algorithm for the optimal basis problem . BIT , 37 ( 3 ) : 591 – 599 .
   Web of Science ®Google Scholar
• Byrd , R. H. , Nocedal , J. and Waltz , R. A. 2006 . “ KNITRO: An integrated package for nonlinear optimization ” . In Large Scale Nonlinear Optimization , 35 – 59 . Heidelberg, Berlin, New York : Springer Verlag .
   Google Scholar
• Ciarlet , P. G. and Raviart , P. A. 1972 . General Lagrange and Hermite interpolation in ℝn with applications to finite element methods . Arch. Ration. Mech. Anal , 46 : 177 – 199 .
   Web of Science ®Google Scholar
• Conn , A. R. , Gould , N. I.M. and Toint , Ph. L. 1992 . “ LANCELOT: a Fortran package for large-scale nonlinear optimization (Release A) ” . Springer Series in Computational Mathematics Vol. 17 , Berlin : Springer .
   Google Scholar
• Conn , A. R. , Gould , N. I.M. and Toint , Ph. L. 2000 . “ Trust-Region Methods ” . Number 01 in MPS-SIAM Series on Optimization Philadelphia, PA : SIAM .
   Google Scholar
• Conn , A. R. , Scheinberg , K. and Toint , Ph. L. 1997 . “ On the convergence of derivative-free methods for unconstrained optimization ” . In Approximation Theory and Optimization: Tributes to M. J. D. Powell , Edited by: Iserles , A. and Buhmann , M. 83 – 108 . Cambridge, , UK : Cambridge University Press .
   Google Scholar
• Conn , A. R. , Scheinberg , K. and Toint , Ph. L. A derivative free optimization algorithm in practice . Proceedings of the 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization . September , St. Louis, MO. pp. 2 – 4 .
   Google Scholar
• Conn , A. R. , Scheinberg , K. and Vicente , L. N. 2008 . Geometry of interpolation sets in derivative free optimization . Math. Program. Ser , B 111 ( 1–2 ) : 141 – 172 .
   Web of Science ®Google Scholar
• Conn , A. R. , Scheinberg , K. and Vicente , L. N. 2009 . “ Introduction to Derivative-free Optimization ” . MPS-SIAM Optimization Series Philadelphia, PA : SIAM .
   Google Scholar
• Custodio , A. L. and Vicente , L. N. 2007 . Using sampling and simplex derivatives in pattern search methods . SIAM J. Optim , 18 : 537 – 555 .
   Web of Science ®Google Scholar
• Custodio , A. L. , Rocha , H. and Vicente , L. N. 2010 . Incorporating minimum Frobenius norm models in direct search . Comput. Optim. Appl , 46 : 265 – 278 .
   Web of Science ®Google Scholar
• Dolan , E. D. and Moré , J. J. 2002 . Benchmarking optimization software with performance profiles . Math. Program , 91 ( 2 ) : 201 – 213 .
   Web of Science ®Google Scholar
• Dolan , E. D. , Moré , J. J. and Munson , T. S. 2006 . Optimality measures for performance profiles . SIAM J. Optim , 16 ( 3 ) : 891 – 909 .
   Web of Science ®Google Scholar
• Fasano , G. , Nocedal , J. and Morales , J.-L. 2009 . On the geometry phase in model-based algorithms for derivative-free optimization . Optim. Meth. Softw , 24 ( 1 ) : 145 – 154 .
   Web of Science ®Google Scholar
• Gould , N. I.M. , Orban , D. and Toint , Ph. L. 2003 . , a constrained and unconstrained testing environment, revisited . ACM Trans. Math. Softw , 29 ( 4 ) : 373 – 394 .
   Web of Science ®Google Scholar
• Gratton , S. , Mouffe , M. and Toint , Ph. L. 2009 . “ Stopping rules and backward error analysis for bound-constrained optimization ” . In Technical Report 09/13, Department of Mathematics, FUNDP , Namur, , Belgium : University of Namur .
   Google Scholar
• Lin , C. and Moré , J. J. 1999 . Newton's method for large bound-constrained optimization problems . SIAM J. Optim , 9 ( 4 ) : 1100 – 1127 .
   Web of Science ®Google Scholar
• Marazzi , M. and Nocedal , J. 2002 . Wedge trust region methods for derivative free optimization . Math. Program. Ser. A , 91 ( 2 ) : 289 – 300 .
   Web of Science ®Google Scholar
• Moré , J. J. and Wild , S. M. 2009 . Benchmarking derivative-free optimization algorithms . SIAM J. Optim , 20 ( 1 ) : 172 – 191 .
   Web of Science ®Google Scholar
• Powell , M. J.D. A direct search optimization method that models the objective and constraint functions by linear interpolation . Advances in Optimization and Numerical Analysis, Proceedings of the Sixth Workshop on Optimization and Numerical Analysis, Oaxaca, Mexico . Edited by: Gomez , S. and Hennart , J. P. Vol. 275 , pp. 51 – 67 . Dordrecht, , The Netherlands : Kluwer Academic Publishers .
   Google Scholar
• Powell , M. J.D. A direct search optimization method that models the objective by quadratic interpolation . Presentation at the 5th Stockholm Optimization Days . Stockholm.
   Google Scholar
• Powell , M. J.D. 1998 . “ The use of band matrices for second derivative approximations in trust region algorithms ” . In Advances in Nonlinear Programming , Edited by: Yuan , Y. 3 – 28 . Dordrecht, , The Netherlands : Kluwer Academic Publishers .
   Google Scholar
• Powell , M. J.D. 2008 . Developments of NEWUOA for minimization without derivatives . IMA J. Numer. Anal , 28 ( 4 ) : 649 – 664 .
   Web of Science ®Google Scholar
• Powell , M. J.D. 2009 . “ The BOBYQA algorithm for bound constrained optimization without derivatives ” . In Technical report, Department of Applied Mathematics and Theoretical Physics , Cambridge, , UK : Cambridge University .
   Google Scholar
• Rios , L. M. and Sahinidis , N. V. 2010 . “ Derivative-free optimization: A review of algorithms and comparison of software implementations ” . In Private communication
   Google Scholar
• Scheinberg , K. and Toint , Ph. L. 2010 . “ Self-correcting geometry in model-based algorithms for derivative-free unconstrained optimization ” . In SIAM J. Optim to appear
   Google Scholar