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- catalog abstract ""Dynamical Search presents a stimulating introduction to a brand new field - the union of dynamical systems and optimization." "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." "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." "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.".
- catalog contributor b11413905.
- catalog contributor b11413906.
- catalog contributor b11413907.
- catalog created "c2000.".
- catalog date "2000".
- catalog date "c2000.".
- catalog dateCopyrighted "c2000.".
- catalog description ""Dynamical Search presents a stimulating introduction to a brand new field - the union of dynamical systems and optimization." "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." "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." "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.".
- catalog description "Includes bibliographical references (p. [211]-215) and indexes.".
- catalog extent "221 p. :".
- catalog identifier "0849303362 (alk. paper)".
- catalog issued "2000".
- catalog issued "c2000.".
- catalog language "eng".
- catalog publisher "Boca Raton : CRC Press,".
- catalog subject "003 21".
- catalog subject "Differentiable dynamical systems.".
- catalog subject "Search theory.".
- catalog subject "T57.97 .P76 1999".
- catalog subject "T57.97 .P76 2000".
- catalog title "Dynamical search : applications of dynamical systems in search and optimization : interdisciplinary statistics / Luc Pronzato, Henry P. Wynn, Anatoly A. Zhigljavsky.".
- catalog type "text".