| Record ID | marc_columbia/Columbia-extract-20221130-005.mrc:450899340:2953 |
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LEADER: 02953fam a2200385 a 4500
001 2349780
005 20220616025302.0
008 990519s1999 flu b 001 0 eng
010 $a 99032954
020 $a0849303362
035 $a(OCoLC)504787735
035 $a(OCoLC)ocn504787735
035 $9APM7630CU
035 $a(NNC)2349780
035 $a2349780
040 $aDLC$cDLC$dNNC$dOrLoB-B
050 00 $aT57.97$b.P76 2000
082 00 $a003$221
100 1 $aPronzato, Luc,$d1959-$0http://id.loc.gov/authorities/names/n96113363
245 10 $aDynamical search :$bapplications of dynamical systems in search and optimisation /$cLuc Pronzato, Henry P. Wynn, Anatoly A. Zhigljavsky.
260 $aBoca Raton, Fla. :$bCRC Press,$c2000.
300 $a221 :$billustrations ;$c24 cm
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
504 $aIncludes bibliographical references and index.
505 00 $g1.$tIntroduction --$g2.$tConsistency --$g3.$tRenormalisation --$g4.$tRates of convergence --$g5.$tLine-search algorithms --$g6.$tEllipsoid algorithms --$g7.$tSteepest-descent algorithm --$g8.$tAppendix.
520 1 $a"Dynamical Search presents a stimulating introduction to a brand new field - the union of dynamical systems and optimization."--BOOK JACKET.
520 8 $a"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.
520 8 $a"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.
520 8 $aAnd 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.
650 0 $aSearch theory.$0http://id.loc.gov/authorities/subjects/sh85119357
650 0 $aDifferentiable dynamical systems.$0http://id.loc.gov/authorities/subjects/sh85037882
700 1 $aWynn, Henry P.$0http://id.loc.gov/authorities/names/n87841481
700 1 $aZhigli͡avskiĭ, A. A.$q(Anatoliĭ Aleksandrovich)$0http://id.loc.gov/authorities/names/n86087174
852 00 $boff,eng$hT57.97$i.P76 2000