User menu

Variable metric random pursuit

Bibliographic reference Stich, Sebastian ; Müller, Christiane L. ; Gärtner, Bernd. Variable metric random pursuit. In: Mathematical Programming, Vol. 156, no.1-2, p. 549-579 (2015)
Permanent URL
  1. Adamczak, R., Litvak, A.E., Pajor, A., Tomczak-Jaegermann, N.: Quantitative estimates of the convergence of the empirical covariance matrix in log-concave ensembles. J. AMS 23, 535–561 (2010). doi: 10.1090/S0894-0347-09-00650-X
  2. Armijo Larry, Minimization of functions having Lipschitz continuous first partial derivatives, 10.2140/pjm.1966.16.1
  3. Brockhoff Dimo, Auger Anne, Hansen Nikolaus, Arnold Dirk V., Hohm Tim, Mirrored Sampling and Sequential Selection for Evolution Strategies, Parallel Problem Solving from Nature, PPSN XI (2010) ISBN:9783642158438 p.11-21, 10.1007/978-3-642-15844-5_2
  4. BROYDEN C. G., The Convergence of a Class of Double-rank Minimization Algorithms 1. General Considerations, 10.1093/imamat/6.1.76
  5. Davidon William C., Variable Metric Method for Minimization, 10.1137/0801001
  6. Fletcher R., A new approach to variable metric algorithms, 10.1093/comjnl/13.3.317
  7. Goldfarb Donald, A family of variable-metric methods derived by variational means, 10.1090/s0025-5718-1970-0258249-6
  8. Goldstein A. A., On Steepest Descent, 10.1137/0303013
  9. Hansen Nikolaus, Ostermeier Andreas, Completely Derandomized Self-Adaptation in Evolution Strategies, 10.1162/106365601750190398
  10. Heijmans Risto, When does the expectation of a ratio equal the ratio of expectations?, 10.1007/bf02927114
  11. Horn Roger A., Johnson Charles R., Matrix analysis, ISBN:9780511810817, 10.1017/cbo9780511810817
  12. Hu T. C., Klee Victor, Larman David, Optimization of Globally Convex Functions, 10.1137/0327055
  13. Jägersküpper Jens, Lower Bounds for Hit-and-Run Direct Search, Stochastic Algorithms: Foundations and Applications ISBN:9783540748700 p.118-129, 10.1007/978-3-540-74871-7_11
  14. Kelley C. T., Implicit Filtering, ISBN:9781611971897, 10.1137/1.9781611971903
  15. Kjellstrom G., Taxen L., Stochastic optimization in system design, 10.1109/tcs.1981.1085030
  16. Leventhal D., Lewis A.S., Randomized Hessian estimation and directional search, 10.1080/02331930903100141
  17. Marti K., Controlled random search procedures for global optimization, Lecture Notes in Control and Information Sciences ISBN:3540166599 p.457-474, 10.1007/bfb0007122
  18. Mathai, A.M., Provost, S.B.: Quadratic forms in random variables: theory and applications. No. 126. In: Statistics: Textbooks and Monographs. New York, Dekker (1992)
  19. Müller Christian L., Sbalzarini Ivo F., Gaussian Adaptation Revisited – An Entropic View on Covariance Matrix Adaptation, Applications of Evolutionary Computation (2010) ISBN:9783642122385 p.432-441, 10.1007/978-3-642-12239-2_45
  20. Nelder J. A., Mead R., A Simplex Method for Function Minimization, 10.1093/comjnl/7.4.308
  21. Nesterov, Y.: Random Gradient-Free Minimization of Convex Functions. Technical report, ECORE (2011)
  22. Powell M. J. D., The NEWUOA software for unconstrained optimization without derivatives, Nonconvex Optimization and Its Applications (2006) ISBN:9780387300634 p.255-297, 10.1007/0-387-30065-1_16
  23. Puntanen Simo, Styan George P. H., Isotalo Jarkko, Matrix Tricks for Linear Statistical Models, ISBN:9783642104725, 10.1007/978-3-642-10473-2
  24. Rosenbrock H. H., An Automatic Method for Finding the Greatest or Least Value of a Function, 10.1093/comjnl/3.3.175
  25. Schumer M., Steiglitz K., Adaptive step size random search, 10.1109/tac.1968.1098903
  26. Shanno D. F., Conditioning of quasi-Newton methods for function minimization, 10.1090/s0025-5718-1970-0274029-x
  27. Stich, S.U.: Convex optimization with random pursuit. ETH Zurich (2014). doi: 10.3929/ethz-a-010377352
  28. Stich Sebastian U., Müller Christian L., On Spectral Invariance of Randomized Hessian and Covariance Matrix Adaptation Schemes, Lecture Notes in Computer Science (2012) ISBN:9783642329364 p.448-457, 10.1007/978-3-642-32937-1_45
  29. Stich S. U., Müller C. L., Gärtner B., Optimization of Convex Functions with Random Pursuit, 10.1137/110853613
  30. Stich, S.U., Müller, C.L., Gärtner, B.: Supporting online material for: variable metric random pursuit. arXiv:1210.5114 (2014)
  31. Wedderburn, J.H.M.: Lectures on Matrices. (Colloquium Publications) AMS, New York (1938)
  32. Wolfe Philip, Convergence Conditions for Ascent Methods, 10.1137/1011036
  33. Wolfe Philip, Convergence Conditions for Ascent Methods. II: Some Corrections, 10.1137/1013035