Research Catalog

Title

Dynamical search : applications of dynamical systems in search and optimisation / Luc Pronzato, Henry P. Wynn, Anatoly A. Zhigljavsky.

Author

Pronzato, Luc, 1959-

Publication

Boca Raton, Fla. : CRC Press, 2000.

Items in the Library & Off-site

Details

Additional Authors

• Wynn, Henry P.
• Zhigli͡avskiĭ, A. A. (Anatoliĭ Aleksandrovich)

Description

221 : illustrations; 24 cm

Summary

• "Dynamical Search presents a stimulating introduction to a brand new field - the union of dynamical systems and optimization."--BOOK JACKET.
• "Certain algorithms that are known to converge can be renormalized or "blown up" at each iteration so that their local behavior can be seen. This creates dynamical systems that we can study with modern tools, such as ergodic theory, chaos, special attractors, and Lyapounov exponents. Furthermore, we can translate the rates of convergence into less studied exponents known as Renyi entropies."--BOOK JACKET.
• "This all feeds back to suggest new algorithms with faster rates of convergence. For example in line-search the Golden Section algorithm can be improved upon with new classes of algorithms that have their own special - and sometimes chaotic - dynamical systems. The ellipsoidal algorithms of linear and convex programming have fast, "deep cut" versions whose dynamical systems contain cyclic attractors.
• And ordinary steepest descent has, buried within, a beautiful fractal that controls the gateway to a special two-point attractor: Faster "relaxed" versions exhibit classical period doubling."--BOOK JACKET. "This unique work opens doors to new areas of investigation for researchers in both dynamical systems and optimization, plus those in statistics and computer science."--BOOK JACKET.

Subjects

• Search theory
• Differentiable dynamical systems

Bibliography (note)

• Includes bibliographical references and index.

Contents

1. Introduction -- 2. Consistency -- 3. Renormalisation -- 4. Rates of convergence -- 5. Line-search algorithms -- 6. Ellipsoid algorithms -- 7. Steepest-descent algorithm -- 8. Appendix.

ISBN

0849303362

LCCN

99032954

OCLC

• 504787735
• ocn504787735

Owning Institutions

Columbia University Libraries