Tài liệu Bài toán đối ngẫu và ứng dụng doc

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Tài liệu Bài toán đối ngẫu và ứng dụng doc

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    ( ) 1 1 max n n f x c x c x= + + → ( ) 1 1 min m m f y b y b y= + + → % 1 1 , 1, , i in n i a x a x b i m ≥     + + ≤ =     =   0 0 , 1, , tuy y i y i m ≤     ≥ =       0 0 , 1, , tuy y j x j n ≥     ≤ =       1 , 1, , ij mj m j a y a y c j n ≥     + + ≤ =     =   ( ) P % ( ) P     !" "#!$"#! " %&'(  )'*+, ,'-# ./  ,'""0/1#*/  ,2 31#/  '(  '-# 45#'  6-/  1##*7891# # :;(  861#*<=>8? '(  863@1#-# A-(B'(  863@'* $'(  <=>'-#B3@CDE F;(  @G>'H'I) 1#"J68?'(  3@' "#! K;(  @G>'H'I) 1#"#!<L68?'(  3@' " → ( ) f y % → → M)3081#N.OO,# ( ) ( ) ( ) ( ) ( ) ( ) 4 4 1 2 3 2 3 4 min 1 2 3 4 2 3 1 2 3 4 3 7 7 1 2 3 2 4 18 1 2 3 6 20 32 1 2 0 3 0 4 0 5 f x x x x x x x x x x x x x x x x x x x x = + → + + − + + + + + ≥ − − − = − ≤ ≥ ≥ ≥ ( ) ( ) ( ) ( ) ( ) : 20 32 18 max 1 2 3 y 3 2 2 6 1 2 3 2y 4 3 7 1 2 3 3y 7 4 8 1 2 3 y 7 6 1 2 3 tuy y 1 P f y y y y y y y y y y y y y = + + → − + ≤ − + ≤ − + + ≤ − + + = − % % ( ) ( ) y 0 9 2 y 0 10 3 ≤ ≥ %P  '(   Q'IP  '(  @G> -7R'(  3@'#J<= >8?"(  P  S, M)30'8)30#BP  '(   T UV %T WV T AV 4T FV :T K ( ) ( ) ( ) ( ) ( ) ( ) 4 4 1 2 3 4 2 3 4 min 1 2 3 4 2 3 1 2 3 4 3 7 7 1 2 3 2 4 18 1 2 3 6 20 32 1 2 0 3 0 4 0 5 tuy y f x x x x x x x x x x x x x x x x x x x x x = + → + + − + + + + + ≥ − − − = − ≤ ≥ ≥ ≥ ( ) ( ) ( ) ( ) ( ) : 20 32 18 max 1 2 3 y 3 2 2 6 1 2 3 2y 4 3 7 1 2 3 3y 7 4 8 1 2 3 y 7 6 1 2 3 tuy y 1 P f y y y y y y y y y y y y y = + + → − + ≤ − + ≤ − + + ≤ − + + = − % % ( ) ( ) y 0 9 2 y 0 10 3 ≤ ≥ M)30%8X8$"P  '(   1#,# ( ) ( ) ( ) ( ) ( ) 15 12 16 10 max 1 2 3 4 3 20 1 1 2 3 4 2 3 2 20 1 2 3 4 2 2 24 2 1 2 3 4 0, 1, ,4 3 6 f x x x x x x x x x x x x x x x x x x j j = + + + → + + + ≤ + + + = + + + ≥ ≥ = → YZ#-1# [\]-^,R!@ ( ) ( ) 1 1 2 2 11 1 12 2 1 21 1 22 2 2 31 1 32 2 3 max 0 1,2 j f x c x j x c x a x a x b a x a x b a x a x b = → ≥ = + + ≤   + ≤   + ≤    O#R$B<_""#I, <L*,R!@1#!)H`B /Q'##/a bc*   DT%T"I=89*,R!@ ^ *  W ≥ O#B,6<L-*,R!@3J 7,R!@'#"I=89,Rd" e^ e^% 11 1 21 2 31 3 a y a y a y+ + 12 1 22 2 32 3 a y a y a y+ +

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