Download Computing Methods in Optimization Problems. Proceedings of a by A. V. Balakrishnan, Lucien W. Neustadt PDF

By A. V. Balakrishnan, Lucien W. Neustadt

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Read or Download Computing Methods in Optimization Problems. Proceedings of a Conference Held at University of California, Los Angeles January 30–31, 1964 PDF

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Extra info for Computing Methods in Optimization Problems. Proceedings of a Conference Held at University of California, Los Angeles January 30–31, 1964

Sample text

930 λ λ 1ι9 . λ7 r,0 0 . „0—. 4 2 7 4— 7 Ζ 0 . 0 5 2 0. 052 0 . 0 6 9 0 . 1 0 0 0 . 1 0 8 0. 385 1. 955 1 9 . 8 5 6 0 . 314 967 1 9 . 9 9 2 0 . 106 0 . 1 1 5 0. 309 925 1 9 . 9 9 0 0 . 4 3 2 9 0 . 0 4 0 0. 035 0 . 0 4 9 0. 098 0 . 1 3 7 0 . 3 0 2 518 1 9 . 9 7 6 0 . 284 268 1 9 . 9 8 2 0 . 270 217 1 9 . 9 9 8 0 . 4 3 4 2 0 . 0 3 9 0. 039 0 . 0 3 9 0 . 1 0 0 0 . 1 6 1 0 . 2 7 0 2 . 2 1 7 1 9 . 9 9 8 0 . 4 3 4 2 0 . 0 3 9 0. 039 0 . 0 3 9 0 . 1 0 0 0 . 1 6 0 0 . 2 7 0 2 . 2 1 8 1 9 . 9 9 8 0 . 4342 0 .

3 - 2 8 8 . 3 -55. 9 4 2 . 7 t h i s t i m e c o n v e r g i n g to 4 2 . 6 7 . O t h e r s t a r t i n g v a l u e s w e r e a l s o t r i e d but w i t h no i m p r o v e m e n t in the y i e l d . T h e s e r e s u l t s a r e a n o t h e r g o o d i l l u s t r a t i o n o f the d i f f i ­ c u l t y in finding a c r i t e r i o n f o r s t o p p i n g a h i l l - c l i m b i n g t e c h ­ n i q u e . T h e r e s u l t s s h o w n in T a b l e 10 w e r e , in f a c t , c o n ­ tinued f o r at l e a s t 4 s t a g e s o f the h i l l - c l i m b without a n y i n ­ c r e a s e in y i e l d (up to the 5th d e c i m a l p l a c e ) w h e r e a s a s s h o w n a b o v e , a c h a n g e o f 0 1% w a s a c h i e v e d b y s t a r t i n g f r o m a different point.

000 . 000 . 008 . 009 . 014 3 COMPUTING METHODS IN OPTIMIZATION PROBLEMS ^< Ο S u b s e q u e n t l y an u p p e r l i m i t Τ =550 C w a s i m p o s e d o n the t e m p e r a t u r e and with t h i s r e s t r i c t i o n the b e s t i s o t h e r m a l y i e l d w a s found t o b e 4 1 . 26 s e e s . 3. FIRST METHOD OF SOLUTION: DISCRETE APPROXIMATION The f i r s t a p p r o a c h w a s t o w r i t e the E q u a t i o n s ( 1 . 3) in finite d i f f e r e n c e f o r m to o b t a i n x 1 lr - x = l,r-l 1 -t r (k lr + k 2r 0 + k_ ) x .

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