A generalized golden-section algorithm for line search

IMA Journal of Mathematical Control and Information

Volumn 15, Issue 2, 1998, Pages 185-214

  Pronzato, Luc ^a   Wynn, Henry P ^b   Zhigljavsky, Anatoly A ^c  

^a UNIVERSITY OF NICE SOPHIA ANTIPOLIS   (France)

^b UNIVERSITY OF WARWICK   (United Kingdom)

^c ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

LYAPUNOV METHODS; MARKOV PROCESSES;

GOLDEN SECTION ALGORITHMS; KOLMOGOROV THEORY; LINE SEARCH; RENYI THEORY;

ALGORITHMS;

EID: 0032095185     PISSN: 02650754     EISSN: None     Source Type: Journal    
DOI: 10.1093/imamci/15.2.185     Document Type: Article

References (11)

1. BARNDORFF-NIELSEN, O. E., JENSEN, J. L., & KENDALL, W. S. (Eds), 1993 Networks and chaos -statistical and probabilistic aspects. Chapman & Hall, London.
2. BEDFORD, T., KEANE, M., & SERIES, C. (Eds), 1991 Ergodic theory, symbolic dynamics, and hyperbolic spaces. Oxford University Press, New York.
3. BOWEN, R. 1975 Equilibrium states and the ergodic theory of Anosov diffeomorphisms. Lecture Notes in Mathematics. Springer, Heidelberg.
4. DU, D.-Z. & HWANG, F. K. 1993 Combinatorial group testing and its applications. World Scientific, Singapore.
5. KIEFER, J. 1957 Optimum sequential search and approximation methods under minimum regularity assumptions. J. Soc. Indust. & Appl. Math. 5(3), 105-36.
6. PRONZATO, L., WYNN, H. P., & ZHIGLJAVSKY, A. A. 1995 Improving on golden-section optimisation for locally symmetric functions. Proceedings of MODA 4 - Advances in Model-Oriented Data Analysis (Ch. P. Kitsos & W. G. Müller, Eds). Physica, Heidelberg. Pp. 285-97.
7. PRONZATO, L., WYNN, H. P., & ZHIGLIJAVSKY, A. A. 1995 Dynamic systems in search and optimisation. CWI Quarterly 8(3), 201-36.
8. PRONZATO, L., WYNN, H. P., & ZHIGHLJAVSKY, A. A. 1995 Stochastic analysis of convergence via dynamic representation for a class of line-search algorithms. Combinotorics, Probability and Computing 6, 205-29.
9. RÉNYI, A. 1965 On the foundations of information theory. Rev. Int. Inst. Statist. 33, 1-14.
10. WYNN, H. P. & ZHIGLJAVSKY, A. A. 1993 Chaotic behaviour of search algorithms. Acta Applicandae Mathematicae 32, 123-56.
11. WYNN, H. P. & ZHIGLJAVSKY, A. A. 1995 Achieving the ergodically optimal convergence rate for a one-dimensional minimization problem, J. of Complexity 11, 196-226.