PSwarm: a hybrid solver for linearly constrained global derivative-free optimization

References

• Abramson , M. A. , Brezhneva , O. A. , Dennis , J. E. and Pingel , R. L. 2008 . Pattern search in the presence of degenerate linear constraints . Optim. Methods Software , 23 : 297 – 319 .
   Web of Science ®Google Scholar
• Anderson , E. , Bai , Z. , Bischof , C. , Blackford , S. , Demmel , J. , Dongarra , J. , Croz , J. D. , Greenbaum , A. , Hammarling , S. , McKenney , A. and Sorensen , D. 1999 . LAPACK Users’ Guide , 3 , Philadelphia, PA : SIAM .
   Google Scholar
• Bergh , F. v. and Engelbrecht , A. P. 2006 . A study of particle swarm optimization particle trajectories . Inform. Sci. , 176 : 937 – 971 .
   Web of Science ®Google Scholar
• Blackford , L. S. , Demmel , J. , Dongarra , J. , Duff , I. , Hammarling , S. , Henry , G. , Heroux , M. , Kaufman , L. , Lumsdaine , A. , Petitet , A. , Pozo , R. , Remington , K. and Whaley , R. C. 2002 . An updated set of basic linear algebra subprograms (BLAS) . ACM Trans. Math. Software , 28 : 135 – 151 .
   Web of Science ®Google Scholar
• Conn , A. R. , Scheinberg , K. and Vicente , L. N. 2009 . Introduction to Derivative-Free Optimization , Philadelphia, PA : SIAM . MPS Book Series on Optimization
   Google Scholar
• DIRECT – A Global Optimization Algorithm. Available at http://www4.ncsu.edu/~ctk/Finkel_Direct
   Google Scholar
• Dolan , E. D. and Moré , J. J. 2002 . Benchmarking optimization software with performance profiles . Math. Program , 91 : 201 – 213 .
   Web of Science ®Google Scholar
• Eberhart , R. and Kennedy , J. A new optimizer using particle swarm theory . Proceedings of the Sixth International Symposium on Micro Machine and Human Science . pp. 39 – 43 . Piscataway, NJ, Nagoya, , Japan : IEEE Service Center .
   Google Scholar
• Fernandes , J. M. , Vaz , A. I.F. and Vicente , L. N. 2008 . Modelling nearby FGK Population I stars: A new form of estimating stellar parameters using an optimization approach , Department of Mathematics, University of Coimbra . Tech. Rep. 08-50
   Google Scholar
• Fourer , R. , Gay , D. M. and Kernighan , B. W. 1990 . A modeling language for mathematical programming . Management Sci , 36 : 519 – 554 .
   Web of Science ®Google Scholar
• GLOBAL Library . Available at http://www.gamsworld.org/global/globallib.htm
   Google Scholar
• Gould , N. I.N. , Orban , D. and Toint , P. L. 2003 . CUTEr (and SifDec), a Constrained and Unconstrained Testing Environment, revisited . ACM Trans. Math. Software , 29 : 373 – 394 . Available at http://cuter.rl.ac.uk/cuter-www
   Web of Science ®Google Scholar
• Ingber , L. 1996 . Adaptative simulated annealing (ASA): Lessons learned . Control Cybernet , 25 : 33 – 54 .
   Google Scholar
• Ji , Y. , Zhang , K. C. and Qu , S. J. 2007 . A deterministic global optimization algorithm . Appl. Math. Comput , 185 : 382 – 387 .
   Web of Science ®Google Scholar
• Jones , D. R. , Perttunen , C. D. and Stuckman , B. E. 1993 . Lipschitzian optimization without the Lipschitz constant . J. Optim. Theory Appl , 79 : 157 – 181 .
   Web of Science ®Google Scholar
• Kennedy , J. and Eberhart , R. Particle swarm optimization . Proceedings of the 1995 IEEE International Conference on Neural Networks . pp. 1942 – 1948 . Piscataway, NJ, Perth, , Australia : IEEE Service Center .
   Google Scholar
• Kolda , T. G. , Lewis , R. M. and Torczon , V. 2003 . Optimization by direct search: New perspectives on some classical and modern methods . SIAM Rev , 45 : 385 – 482 .
   Web of Science ®Google Scholar
• Kolda , T. G. , Lewis , R. M. and Torczon , V. 2006 . Stationarity results for generating set search for linearly constrained optimization . SIAM J. Optim , 17 : 943 – 968 .
   Web of Science ®Google Scholar
• Lewis , R. M. and Torczon , V. 2000 . Pattern search methods for linearly constrained minimization . SIAM J. Optim , 10 : 917 – 941 .
   Web of Science ®Google Scholar
• Lucidi , S. , Sciandrone , M. and Tseng , P. 2002 . Objective-derivative-free methods for constrained optimization . Math. Program , 92 : 37 – 59 .
   Web of Science ®Google Scholar
• MATLAB, The MathWorks Inc. Available at http://www.mathworks.com
   Google Scholar
• Michalewicz , Z. 1994 . Evolutionary computation techniques for nonlinear programming problems . Int. Trans. Oper. Res , 1 : 223 – 240 .
   Google Scholar
• Michalewicz , Z. 1996 . Genetic Algorithms + Data Structures = Evolution Programs , 3 , Berlin : Springer .
   Google Scholar
• Moré , J. J. and Wild , S. M. 2009 . Benchmarking derivative-free optimization algorithms . SIAM J. Optim , 20 : 172 – 191 .
   Web of Science ®Google Scholar
• Neumaier , A. The COCONUT benchmark . Available at http://www.mat.univie.ac.at/~neum/glopt/coconut/Benchmark/Benchmark.html
   Google Scholar
• NOMADm Optimization Software. Available at http://www.gerad.ca/NOMAD/nomadm.html
   Google Scholar
• The NOMAD Project. Available http://www.gerad.ca/NOMAD
   Google Scholar
• Parpas , P. , Rustem , B. and Pistikopoulos , E. N. 2006 . Linearly constrained global optimization and stochastic differential equations . J. Global Optim , 36 : 191 – 217 .
   Google Scholar
• Pintér , J. 2002 . Handbook of Global Optimization , Edited by: Pardalos , P. M. and Romeijn , H. E. 515 – 569 . Dordrecht : Kluwer Academic Publishers . Nonconvex Optimization and Applications, Vol. 62, chap. 15
   Google Scholar
• Rubin , P. A. 1984 . Generating random points in a polytope . Comm. Statist. Simulation Comput , 13 : 375 – 396 .
   Web of Science ®Google Scholar
• Runarsson , T. P. and Yao , X. 2000 . Stochastic ranking for constrained evolutionary optimization . IEEE Transactions on Evolutionary Computation , 4 : 284 – 294 .
   Web of Science ®Google Scholar
• Schutte , J. F. and Groenwold , A. A. 2005 . A study of global optimization using particle swarms . J. Global Optim , 31 : 93 – 108 .
   Web of Science ®Google Scholar
• Vanderbei , R. J. Benchmarks for Nonlinear Optimization . Available at http://www.princeton.edu/~rvdb/bench.html
   Google Scholar
• Vaz , A. I.F. and Vicente , L. N. 2007 . A particle swarm pattern search method for bound constrained global optimization . J. Global Optim , 39 : 197 – 219 .
   Web of Science ®Google Scholar
• Zhang , Y. and Gao , L. 2003 . On numerical solution of the maximum volume ellipsoid problem . SIAM J. Optim , 14 : 53 – 76 .
   Web of Science ®Google Scholar