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By Jean-Luc Chabert, C. Weeks, E. Barbin, J. Borowczyk, J.-L. Chabert, M. Guillemot, A. Michel-Pajus, A. Djebbar, J.-C. Martzloff

ISBN-10: 3540633693

ISBN-13: 9783540633693

A resource publication for the background of arithmetic, yet one that bargains a distinct point of view via focusinng on algorithms. With the improvement of computing has come an awakening of curiosity in algorithms. frequently overlooked through historians and sleek scientists, extra excited about the character of suggestions, algorithmic approaches prove to were instrumental within the improvement of primary principles: perform ended in idea simply up to the opposite direction around. the aim of this publication is to supply a old historical past to modern algorithmic perform.

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Jean-Luc Chabert, C. Weeks, E. Barbin, J. Borowczyk, J.-L.'s A History of Algorithms: From the Pebble to the Microchip PDF

A resource ebook for the heritage of arithmetic, yet one that bargains a unique point of view by means of focusinng on algorithms. With the advance of computing has come an awakening of curiosity in algorithms. frequently missed through historians and glossy scientists, extra all for the character of recommendations, algorithmic tactics end up to were instrumental within the improvement of primary principles: perform ended in thought simply up to the opposite direction around.

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7) sia soddisfatta e che valgano le ipotesi (H1 ) (H2 ). 10) e sia {xk } la successione dei punti di minimo non vincolato delle funzioni P (x; ck ). Allora, per ogni k si ha: (a) P (xk ; ck ) ≤ f (x∗ ); (b) ψ(xk+1 ) ≤ ψ(xk ); (c) f (xk+1 ) ≥ f (xk ); (d) P (xk+1 ; ck+1 ) ≥ P (xk ; ck ). Dimostrazione. Essendo xk un punto di minimo non vincolato di P (x; ck ), tenendo conto del fatto che ψ(x) = 0 per x ∈ S, si ha: P (xk ; ck ) = minn f (x)+ck ψ(x) ≤ min f (x)+ck ψ(x) = min f (x) = f (x∗ ), x∈R x∈S x∈S il che prova la (a).

Punto di sella Se risulta ∇f (x ) = 0 e la matrice Hessiana ∇2 f (x ) `e indefinita (ossia, esistono vettori d per cui dT ∇2 f (x )d > 0 e altri per cui dT ∇2 f (x )d < 0) allora si pu` o escludere che x sia un punto di minimo o di massimo locale e il punto x `e un punto di sella. Un punto di sella `e, in generale, un punto stazionario in corrispondenza al quale esistono sia direzioni di discesa sia direzioni di salita. 3. Si consideri la funzione f : R2 → R definita come segue: f (x) = x21 − x22 .

Dal punto di vista algoritmico, una condizione necessaria pu` o servire a restringere l’insieme in cui ricercare le soluzioni del problema originario e a costruire algoritmi finalizzati al soddisfacimento di tale condizione. Tutti gli algoritmi che studieremo nel seguito sono infatti costruiti per determinare punti che soddisfano una condizione necessaria di ottimo. : Metodi di ottimizzazione non vincolata. © Springer-Verlag Italia 2011 36 2 Condizioni di ottimo per problemi non vincolati Una condizione sufficiente pu` o servire a dimostrare che un punto ottenuto per via numerica sia una soluzione ottima (locale o globale) del problema.

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A History of Algorithms: From the Pebble to the Microchip by Jean-Luc Chabert, C. Weeks, E. Barbin, J. Borowczyk, J.-L. Chabert, M. Guillemot, A. Michel-Pajus, A. Djebbar, J.-C. Martzloff


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