Direction Choice for Accelerated Convergence in Hit-and-Run Sampling

Published Online:https://doi.org/10.1287/opre.46.1.84

References

  • Bélisle C. J. P. , Romeijn H. E. , Smith R. L. Hit-and-run algorithms for generating multivariate distributions. Math. O. R. (1993) 18 255 266 LinkGoogle Scholar
  • Berbee H. C. P. , Boender C. G. E. , Rinnooy Kan A. H. G. , Scheffer C. L. , Smith R. L. , Telgen J. Hitand-run algorithms for the identification of nonredundant linear inequalities. Math. Programming (1987) 37 184 207 CrossrefGoogle Scholar
  • Billingsley P. Probability and Measure (1986) (John Wiley & Sons, New York) Google Scholar
  • Boneh A. , Golan A. Constraints' redundancy and feasible region boundedness by random feasible point generator (RFPG). (1979) . Presented at the Third European Congress on Operations Research (EURO III), Amsterdam Google Scholar
  • Brooks S. H. A discussion of random methods for seeking maxima. Opns. Res. (1958) 6 244 251 LinkGoogle Scholar
  • Chen M. , Schmeiser B. Performance of the Gibbs, hit-and-run and metropolis samplers. J. Computational Graphical Statist. (1993) 2 251 272 CrossrefGoogle Scholar
  • Cowles M. K. , Carlin B. P. Markov chain Monte Carlo convergence diagnostics: A comparative review. (1994) . Technical report 94-008. Division of Biostatistics, School of Public Health, University of Minnesota Google Scholar
  • Dixon L. C. W. , Szegö G. P. Towards Global Optimization (1975) (North-Holland, Amsterdam) Google Scholar
  • Dixon L. C. W. , Szegö G. P. Towards Global Optimization 2 (1978) (North-Holland, Amsterdam) Google Scholar
  • Doob J. L. Stochastic Processes (1953) (John Wiley & Sons, New York) Google Scholar
  • Gelfand A. E. , Smith A. F. M. Sampling-based approaches to calculating marginal densities. J. Amer. Statist. Assoc. (1990) 85 398 409 CrossrefGoogle Scholar
  • Gelman A. , Rubin D. B. Inference from iterative simulation using multiple sequences. Statist. Sci. (1992) 7 457 511 CrossrefGoogle Scholar
  • Geman S. , Geman D. Stochastic relaxation, Gibbs distributions, and the bayesian restoration of images. IEEE Trans. Pattern Anal. Machine Intelligence (1984) 6 721 741 CrossrefGoogle Scholar
  • Geyer C. J. Practical Markov chain Monte Carlo. Statist. Sci. (1992) 7 4 473 483 CrossrefGoogle Scholar
  • Gilks W. R. , Roberts G. O. , George E. I. Adaptive direction sampling. The Statistician (1994) 43 179 189 CrossrefGoogle Scholar
  • Hammersley J. M. , Handscomb D. C. Monte Carlo Methods (1964) (Methuen & Co. Ltd., London) CrossrefGoogle Scholar
  • Hastings W. K. Monte Carlo sampling methods using Markov chains and their applications. Biometrika (1970) 57 97 109 CrossrefGoogle Scholar
  • Helms L. L. Introduction to Potential Theory (1969) (John Wiley & Sons, New York) Google Scholar
  • Karwan M. H. , Lotfi V. , Telgen J. , Zionts S. Redundancy in Mathematical Programming (1983) (Springer-Verlag, Berlin) CrossrefGoogle Scholar
  • Knuth D. E. The Art of Computer Programming (1981) 2 2nd ed. (Addison-Wesley, Reading, Massachusetts) Google Scholar
  • Metropolis N. , Rosenbluth A. W. , Rosenbluth M. N. , Teller A. H. , Teller E. Equations of state calculations by fast computing machines. J. Chemical Phys. (1953) 21 1087 1092 CrossrefGoogle Scholar
  • Patel N. R. , Smith R. L. , Zabinsky Z. B. Pure adaptive search in Monte Carlo optimization. Math. Programming (1988) 43 317 328 CrossrefGoogle Scholar
  • Rinnooy Kan A. H. G. , Timmer G. T. Stochastic global optimization methods—Part I: Clustering methods. Math. Programming (1987) 39 27 56 CrossrefGoogle Scholar
  • Roberts G. O. , Gilks W. R. Convergence of adaptive direction sampling. J. Multivariate Anal. (1994) 49 287 298 CrossrefGoogle Scholar
  • Rubinstein R. Y. Simulation and the Monte Carlo Method (1981) (John Wiley & Sons, New York) CrossrefGoogle Scholar
  • Schmeiser B. W. , Oren T. I. , Shub C. M. , Roth P. F. Random variate generation: A survey. Simulation with Discrete Models: A State of the Art View (1981) (IEEE, New York) 79 104 Google Scholar
  • Schmeiser B. W. , Chen M. On hit-and-run Monte Carlo sampling for evaluating multidimensional integrals. (1991) . Report SMS91-1, Department of Statistics, Purdue University Google Scholar
  • Solis F. J. , Wets R. J.-B. Minimization by random search techniques. Math. O. R. (1981) 6 19 30 LinkGoogle Scholar
  • Sommerville D. M. Y. An Introduction to the Geometry of N Dimensions (1958) (Dover Publications, Inc., New York) Google Scholar
  • Smith R. L. Monte Carlo techniques for generating random feasible solutions to mathematical programs. (1980) Washington, DC . Presented at the ORSA/TIMS Conference Google Scholar
  • Smith R. L. Efficient Monte Carlo procedures for generating points uniformly distributed over bounded regions. Opns. Res. (1984) 32 1296 1308 LinkGoogle Scholar
  • Tanner M. A. , Wong W. H. The calculation of posterior distributions by data augmentation. J. Amer. Statist. Assoc. (1987) 82 528 541 CrossrefGoogle Scholar
  • Telgen J. Private communication with A. Boneh. (1980) Google Scholar
  • Zabinsky Z. B. , Smith R. L. Pure adaptive search in global optimization. Math. Programming (1992) 53 323 338 CrossrefGoogle Scholar
  • Zabinsky Z. B. , Smith R. L. , McDonald J. F. , Romeijn H. E. , Kaufman D. E. Improving hit and run for global optimization. J. Global Optim. (1993) 3 171 192 CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.